Rectangular parallelepiped
1. Two edges of a rectangular parallelepiped coming from the same vertex are 3 and 4. The surface area of this parallelepiped is 94. Find the third edge coming from the same vertex.
2. Two edges of a rectangular parallelepiped extending from the same vertex are equal to 1, 2. The surface area of the parallelepiped is 16. Find its diagonal.
3. A rectangular parallelepiped is described around a unit sphere. Find its surface area.
4. The area of the face of a rectangular parallelepiped is 12. The edge perpendicular to this face is 4. Find the volume of the parallelepiped.
5. The volume of a rectangular parallelepiped is 24. One of its edges is 3. Find the area of the face of the parallelepiped perpendicular to this edge.
6. The volume of a rectangular parallelepiped is 60. The area of one of its faces is 12. Find the edge of the parallelepiped perpendicular to this face.
7. Three edges of a rectangular parallelepiped coming from one vertex are equal to 4, 6, 9. Find the edge of a cube of equal size.
8. Two edges of a rectangular parallelepiped extending from the same vertex are equal to 2, 4. The diagonal of the parallelepiped is equal to 6. Find the volume of the parallelepiped.
9. Two edges of a rectangular parallelepiped coming from one vertex are equal to 2, 3. The volume of the parallelepiped is 36. Find its diagonal.
10. The diagonal of a rectangular parallelepiped is equal to and forms angles of 30, 30 and 45 with the planes of the faces of the parallelepiped. Find the volume of the parallelepiped.
11. The edges of a rectangular parallelepiped extending from one vertex are 1, 2, 3. Find its surface area.
12. The two edges of a rectangular parallelepiped extending from the same vertex are 2, 4. The diagonal of the parallelepiped is 6. Find the surface area of the parallelepiped.
13. Two edges of a rectangular parallelepiped extending from one vertex are equal to 1, 2. The volume of the parallelepiped is 6. Find its surface area.
14. Find the angle of a rectangular parallelepiped for which, . Give your answer in degrees.
15. Find the angle of a rectangular parallelepiped for which =4, =3, =5. Give your answer in degrees.
16.V rectangular parallelepiped it is known that, . Find the length of the edge.
17. In a rectangular parallelepiped, edge, edge, edge. Point - the middle of the edge Find the area of the section passing through the points and.
18.. In a rectangular parallelepiped the lengths of the edges are known: , . Find the area of the section passing through the vertices and.
19. In a rectangular parallelepiped, the lengths of the edges are known: AB = 3, AD = 5, AA1 = 12. Find the cross-sectional area of the parallelepiped by the plane passing through points A, B and C1.
20. In a rectangular parallelepiped ABCDA1B1C1D1 edge BC = 4, edge edge BB1 = 4. Point K is the middle of edge CC1. Find the area of the section passing through points B1, A1 and K.
21. In a rectangular parallelepiped ABCDA1B1C1D1 edge CD = 2, edge edge CC1 = 2. Point K is the middle of edge DD1. Find the area of the section passing through points C1, B1 and K.
Type C tasks – 2,
taken from various Unified State Exam materials 2010.
1.
The lengths of the edges AB = 3, AD = 4, CC 1 = 4 are known. Find the angle between the planes BDD 1 and AD 1 B 1.
(Another option: AB = 5, AD = 12, CC 1 = 4 or else: AB = 8, AD = 6, CC 1 = 2)
2
.
In a rectangular parallelepiped ABCDA 1B 1C 1D 1 known ribs: AB= 5, AD=12, CC 1 = 3. Find the angle between the planes BDD 1 and AD 1 B 1 .
3
.
In the right hexagonal prism ABCDEFA 1 B 1 C 1 D 1 E 1 F 1 the side of the base is 3 and the height is 1. Find the angle between the line F 1 B 1 and the plane AF 1 C 1.
(Another option: find the distance from point C to straight line SA;
Another option: find the distance from point C to straight line SF).
4.
In the cube ABCDA 1 B 1 C 1 D 1 all edges are equal to 1. Find the distance from point C to line BD 1 (other option: to line AD 1).
In a regular hexagonal SABC pyramid DEF, the sides of the base are equal to 1 and the side edges are equal to 2, find the cosine of the angle between the lines SB and AD.
In the right triangular prism ABCA 1 B 1 C 1 height is 1 and base edge is 2. Find the distance from point A 1 to line BC 1.
7.
At the base of the quadrangular pyramid SABCD lies a square with side . The lengths of all side edges are equal to 3, point M is the middle of edge AS. A plane is drawn through straight line BM parallel to diagonal AC. Determine the magnitude of the acute angle (in degrees) between this plane and the SAC plane.
Straight base quadrangular prism is a rhombus with an acute angle of 60 degrees. Find sharp corner between larger diagonal the lower base and the diagonal of the side face crossing with it, if the ratio of the height of the prism to the side of its base is equal to 
.
9.
, SC = 17. (Another option: AB = 
, SC = 17;).
Find the angle formed by the base plane and the lines AS and BC.
10.
In the right triangular pyramid SABC with base ABC known edges AB = 
, SC = 10. Point N is the middle of edge BC. Find the angle between the base plane and the straight line AT, where T is the midpoint of the segment SN)
(Another option: AB = 
, SC = 5. Point N is the middle of edge CD).
11.
In a regular triangular pyramid SABC with base ABC the edges are known: AB = 
, SC = 34. (Another option: AB = 
, SC = 25). Find the angle formed by the base plane and the straight line AM, where M is the point of intersection of the medians of the face SBC.
12.
A.A. 1 =
4, A 1 D 1 =
6, C 1 D 1 = 6, find the tangent of the angle between the plane ADD 1 and straight E.F. passing through the middle of the ribs AB and B 1 C 1 .
13.
In a rectangular parallelepiped ABCDA 1 B 1 C 1 D 1 , in which AB = 4, BC = 6, CC 1 = 4, find the tangent of the angle between the plane ABC and straight E.F. passing through the middle of the ribs A.A. 1 and C 1
D 1 .
14.
In a rectangular parallelepiped ABCDA 1
B 1
C 1
D 1
, which one A.A. 1 =
4, A 1
D 1 =
6, C 1
D 1 = 6, find the tangent of the angle between the plane ADD 1 and straight E.F. passing through the middle of the ribs AB and B 1 C 1 .
15
.
In the rectangular parallelepiped ABCDA 1 B 1 C 1 D 1, find the angle between the plane AA 1 C and the straight line A 1 B, if AA 1 = 3, AB = 4. BC = 4.
(Another option: plane A 1 BC and straight line BC 1, if AA 1 = 8, AB = 6. BC = 15).
16.
In a tetrahedron ABCD, all edges of which are equal to 1, find the distance from the point A to a straight line passing through a point B and middle E ribs CD.
17
.
In the right quadrangular pyramid SABCD, the side of the base is equal to 1, and the side edge is equal to 
Find the distance from the point C to a straight line S.A.
18.
To the diagonal A 1 C of the cube ABCDA 1 B 1 C 1 D 1 we draw perpendiculars from the midpoints of the edges AB And AD.
Find the angle between these perpendiculars.
(Another option: draw perpendiculars from vertices A and B).
19
.
Diagonal A 1 C of cube ABCDA 1 B 1 C 1 D 1 serves as an edge dihedral angle, the edges of which pass through the midpoints of the edges AB and DD 1. Find the value of this angle.
(Another option: the faces pass through vertices B and D)
Publicat pe 6 ian. 2014
The cross-sectional area is the root of 133. Task C2 is solved by mathematics tutor A.E. Sultanov Unified State Exam expert.
plus.google.com/b/105020197419992802237/ Preparation for the Unified State Exam in mathematics
Demo version GIA 2013 and GIA 2014 in mathematics in new form
GIA Problem 9-13. IN isosceles triangle ABC with base AC external corner at vertex C is 123.
In the rectangular parallelepiped ABCDA1B1C1D1 the following edges are known: AB = 3, AD = 2, AA1 = 5.
Point O belongs to edge BB1 and divides it in a ratio of 2:3, counting from vertex B.
Option for independent decision:
(send your solution to tutor A.E. Sultanov - Unified State Exam expert - for verification)
In the rectangular parallelepiped ABCDA1B1C1D1 the edges AB=5, AD=4, AA1=9 are known.
Point O belongs to edge BB1 and divides it in the ratio 4:5, counting from vertex B.
Find the cross-sectional area of this parallelepiped by a plane passing through points A, O and C1.
In a rectangular parallelepiped, the section of the parallelepiped passes through the points and forms an angle alpha with the plane.
And finally, we get: Answer: 112, a math tutor will solve the exam math on a mobile phone during the exam.
A rectangular parallelepiped in lessons with a tutor.
A collection of problems for a math tutor on a paralleleped.
The sides of the base in a rectangular parallelepiped are 3 and 4 cm.
Its diagonal makes an alpha angle with the smaller side face.
In a rectangular parallelepiped - School Knowledge.
In a rectangular parallelepiped there are many Unified State Exam problems.
In the rectangular parallelepiped ABCDA1B1C1D1 it is known that AC1 = root of 50, BB1 = 3, B1C1 = 4. Find the length of the edge DC.
Bodies in space: prism, parallelepiped, cube
Study with the best tutors online! We have already drawn a square of any diagonal in a rectangular parallelepiped equal to the sum squares of its three linear dimensions.
Rectangular parallelepiped. Tutors know his property. In a rectangular parallelepiped, the square of any diagonal is equal to the sum of the squares of its three dimensions. Proof.
What is a parallelepiped?
Mathematics tutor Dmitrov. Articles. Formulas and theory. A right parallelepiped whose bases are rectangles is called a cuboid.
Commentarii
Alexey Uchitelsky Help in mathematics, physics, chemistry, solving tests. vk.com/repetitor007tutor Tutors. Find a tutor based on the database. Join a team of tutors. Plot a function graph online. Calculate the integral online. Solving problems and tests. Test on "Informatics" - solve test Let's help! Attached files: 1 file. Download the document View the text.docx file. Test option No. 4. discipline: Computer Science. Completed by: 1st year student. Test in computer science High-quality knowledge of students! Choose who to entrust your education to based on an honest rating of teachers, compiled only on the basis of the experience of other students. Financial security for tutors! You are guaranteed to receive payment for the lesson conducted - we are a guide between the students and you, insuring against dishonest actions. Online schedule Plan and control your class schedule from your personal account.
Alexey Pokrovsky Tutor in mathematics, physics, computer science. Red Diploma from MIPT (Moscow Institute of Physics and Technology) Honours. skype-school.blogspot.ru/2014/02/skype-tutor-school.html Excellent Online tutor via Skype - Skype online tutor school! Mathematics Tutors are not some kind of tutoring agency, private teachers are Mathematics Tutors. Real scientists and devotees! Math tutors, higher mathematics(Moscow) Private tutor in mathematics in Moscow. Preparation for the Unified State Exam 2014, State Examination. Mathematics for students in grades 7-11, applicants, students. Selection of great math tutors in Moscow. Online Preparation to the GIA and Unified State Examination. A tutor in mathematics, algebra or geometry may also be needed for those who do not understand well difficult topic, which, for example, the teacher did not have time to explain. Tariverdiev: Would you like to order a test? You can buy a test paper to order and inexpensively in Moscow from us! Tutor Alexey Diplomov told Kursova. - Good afternoon. Would you like to let Jesus Christ into your home? - Jesus Christ can come in, and you go to the tutor from here.
Lara Tarasova Study with the best tutors via the Internet! We have already conducted 234 lessons. xn-----8kcavadbvfwtcwblelf1bbid.xn--p1ai/fismat/obraschenie_distantsionnogo_repetitora.html Learning from Teacher Alexey - a distance tutor in mathematics online via Skype - Skype! Example: In a rectangular parallelepiped, the square of any diagonal is equal to the sum of the squares of its three linear dimensions. Tutor Online math tutor The cross-sectional area is the root of 133, not 61. Task C1 C2 Mathematics tutor sites. Professional Services mathematics tutor in Moscow. Let's consider the solution to the following problem: In a rectangular parallelepiped, mine Reviews! Rectangular parallelepiped. Property you need to know! The tutors will tell you. In a rectangular parallelepiped, the square of any diagonal is equal to the sum of the squares of its three dimensions. The proof is on online lesson. In a rectangular parallelepiped. - School Knowledge with a tutor. In a rectangular parallelepiped. In the rectangular parallelepiped ABCDA1B1C1D1 it is known that BD1=3, CD=2, AD=2. Find the length of edge AA1. What is a parallelepiped? A right parallelepiped whose bases are rectangles is called a cuboid. Mathematics tutor in Dmitrov for schoolchildren and students.
Alexey Uchitelsky Mathematics Tutor - Section 3. Tasks 8 for exams. real-gia.blogspot.ru/p/blog-page.html GIA math tutors! We help solve mathematics, economics, physics, mechanics. Online solution tasks! The cross-sectional area of a rectangular parallelepiped is the root of 133. Task C2 is solved by a mathematics tutor A.E. Sultanov Unified State Exam expert. In a rectangular parallelepiped, the section of the parallelepiped passes through the points and forms an angle alpha with the plane. And finally, we get: Answer: 112, a math tutor will solve the exam math on a mobile phone during the exam. A rectangular parallelepiped in lessons with a tutor. A collection of math tutor problems on a parallelepiped. Math tutor. Cheat sheets for the Unified State Exam. In a rectangular parallelepiped, a section is drawn through the edge of the lower base and the intersection point of the diagonals of the opposite side face. In a rectangular parallelepiped, the sides of the base are 7 dm and 24 dm. The base of the parallelepiped is a rectangle with sides a1 = 7 in. and a2 = 24 in. 38. Find the surface of a rectangular parallelepiped based on its three dimensions: 10 cm, 22 cm, 16 cm. The base of the parallelepiped - tutor announcements: Mathematics. Community of private tutors. More than 600 options. Free selection! Association of Moscow Tutors More than 150 tutors in Moscow and the region. Free selection of tutors. Dubrovka Moscow tutor database Convenient search for tutors in Moscow: by price, by metro station. For free! Tutors from 1400 rub. Come in! Tutor for any subject. Free selection! Fast. 100% guarantee! Very good tutor.
Found a mistake in the teacher's decision? No? moskva-repetitor.blogspot.ru/2014/01/blog-post.html Tutors for all school subjects And foreign languages: A new order for teaching mathematics and English has appeared on the portal “A Tutor - ATutor” ➊ The area of a trapezoid with bases 3 and 5 and height 3 is equal to 4∙3 = 12. ➋ Next, the directed areas are subtracted: |3 - 12| = 9, 7 - 3 = 4. ➌ The sum of their squares = 9² + 4² + 6² = 81 + 16 + 36 = 133. ➍ Sectional area = √133. Everything fits! ➎ + !!!
Sorry that the money is wet,” the lady said to the seller in the fur store. “My husband, a mathematics and physics teacher, cried so much when he gave them to me. Help, I really need it, use the equation heat balance, equate to Joule Lenz's law, express voltage. You can also order ready-made paid solution. Write in PM if relevant. I like to study online via Skype. Help me decide. For example, with lambda = 1, the solution will look like: How many degrees will an iron cube weighing 0.1 kg, freely falling vertically from a height of 230 m, heat up by the time it hits the ground, if the average value of the air resistance force is 0.2 R? Specific heat iron is 460 J/kg K. determine the amount of heat required to heat 1 mole of an ideal monatomic gas by 20 K at constant pressure
Imagists and futurists tutors. Yesenin was once asked by mathematicians: “What is the reason for the sharp hostile relationship between imagists and physics teachers - futurists?" Yesenin laconically replied: "The mathematics and physics teachers are robbing me." The fact is that Yesenin quite sincerely believed that futurist tutors use the same mathematical and poetic devices, as he does, but to divert attention they saturate them with urbanisms, parabolas and hyperbolas. No one and nothing could convince Yesenin on this issue of tutoring in physics and mathematics.
How to pass the Unified State Exam in mathematics in 2015? Andrey. Interesting. That is why I decided to introduce you to Alexey and Natalya, who write theses with all their hearts. Course work. mathematical analysis. An anecdote is a joke of humor: The main points of the government's anti-crisis plan: - reduce the price of vodka - allow swearing in the USE mathematics exam 2015: theory, solution, answers. How to decide. #ege info Theory of the Unified State Exam 2015. All considered necessary formulas, theorems, postulates that must be mastered in order to successfully solve the type of geometry problems on the real Unified State Exam. The theory has been collected and justified taking into account changes in structure of the Unified State Exam in mathematics in 2015. Solution for mathematics Maltsev Unified State Exam 2015
Jokes and humor of mathematicians: After completing your studies, go to America. Let their economy collapse there. Our tutors at MIPT laughed!
Tutors in Mathematics Moscow | TEACH me the Unified State Exam. #msk #nauchi Tutor mathematics Moscow Repetitor Centers include mathematics If you need good tutor in mathematics in Moscow or in any other city in the Moscow region, then simply use the search on the website or entrust the selection to the administrator. Mathematics tutors in Moscow - Tutor Plus Skype!
This was told by online physics and mathematics tutor Arkady Kursovoy. Every day the tutor comes to work at nine o'clock in the morning. At this time, the cleaning lady, a woman about 54-55 years old, who cleans all the offices of math tutors before the start of the working day, usually leaves. Almost every day the mathematician meets her at the entrance to the office center building. She is always followed by a man (also a physics tutor) who carries large plastic bags of garbage. That tutor is already old. I always thought that this was not a tutor, but just a cleaner, a full-time employee of the business department. But at the same time, the physics tutor is always decently dressed, and after our morning meeting he no longer appears. Just recently I found out that it turns out that this is the husband of our cleaning lady. A man works in a completely different place, but every morning at seven o’clock he arrives with his wife and helps her clean up and takes out the trash, after which he goes to his work. Made the tutors think. (Unified State Examination, 2015) Near an acute angle triangle ABC a circle with center O is described. On the continuation of the segment AO, point K is marked beyond point O so that ZBAC + ZAKC = 90◦. Prove that the quadrilateral OBKC is cyclic. Find the radius of the circle circumscribed around the quadrilateral OBKC if cos ZBAC == 3/5 and BC = 48. Problem C4 with the Unified State Examination in Mathematics 2015. Tutor's solution - Sultanov's method. (MIOO, KIM 2015) On the diagonal of the parallelogram we took a point different from its middle. From it, perpendiculars were lowered onto all sides of the parallelogram (or their extension). Prove that the quadrilateral formed by the bases of these perpendiculars is a trapezoid. Find the area of the resulting trapezoid if the area of the parallelogram is 16 and one of its angles is 60◦.
Problem c2. Preparation for the Unified State Exam 2017 in mathematics. Trigonometry problems - level B. Preparation for the Unified State Exam in mathematics How to add fractions with different denominators? po #trigonometrii #ege-po-matematike For students with an average or weak level of knowledge in trigonometry, a mathematics tutor breaks down the preparation for C1 problems with the Unified State Exam into several stages. One of them is solving equations by changing a variable. stereometry Unified State Exam task mathematics profile A.L Semenov I.V Yashchenko geometry stereometry problem 14, trigonometric equations| Preparation for the Unified State Exam in mathematics
Cool video! Thanks a lot. other references. Problem book on heat and mass transfer. IN textbook Problems are presented for all sections of the Heat and Mass Transfer course. Problem book on heat and mass transfer You can download the book in class. Your tutor Alexey #tutors Unified State Exam 2015 mathematics. Tasks. Answers. Solutions. Educational system Let's solve the problem from Task C3 to prepare for the Unified State Exam in mathematics: Solve the system of inequalities The majorant method is used when solving non-standard inequalities problems that cannot be solved using standard techniques Unified State Exam courses in mathematics I want to know Math Skype address and phone number, Maryino metro station, Revolution Square - via Skype online. Mini groups up to 3 people. All things. Center of Moscow. Get ready with us! Courses Unified State Exam Reviews students Unified State Exam teachers Unified State Exam results Community of private tutors. More than 680 options. Free selection! Mathematics Book of reviews Russian language Tutors without intermediaries #legko
Nastya Ibragimovna Putina - Student of ZFTSH MIPT - asks to solve mathematics: The second, simpler way to solve one problem in stereometry. The harvested materials will be enough to operate two workshops for 10 days or one first workshop for 30 days. How many days would these materials last for one 10-day operation or one first workshop for 30 days? #tekstovye #zadachi #smesi na #work Tutor's answers: The prepared materials are enough for two teachers to work with. Daily work, temporary The most complete database of vacancies! Here you will find what you need. South-West ad for the request “For how many days”
I have a few questions. 1) This is the title of the topic: Tell me, how can I pass the Unified State Exam if I graduated from school 5 years ago? 2) What is needed for this (documents)? 3) Are there any good Tutors? Don't suggest Kolpakov. You can take the Unified State Exam at the university that you are going to conquer. If you have already received higher education, then the second higher education is only for a fee, there are options for accelerated training. I recommend Tutor Alexey Uchitel. How to pass the Unified State Exam after finishing school a long time ago. How to pass the Unified State Exam. Forum about education and science.
An abridged version of my book “Tips for those taking the Unified State Exam in Physics,” which is currently being prepared for publication. Solving inequalities with fractions. Recommendations are given based on the author’s personal long-term experience; The works of other authors are taken into account. How to pass the Unified State Exam! Advice from a psychologist - My files - File catalog - MIPT, MSLU, MSU. Follow the rules of behavior during the exam! Do not shout out from your seat - if you want to ask a question to the organizer conducting the Unified State Exam in the audience, raise your hand. How to pass the Unified State Exam with 100 points: advice from teachers and secrets of former students.
News of the day. Russian mathematician Grigory Perelman moved to live in Sweden Famous Russian mathematicianהִירשׁ פּעֶרעֶלמאַן Grigory Perelman, who proved the Poincaré conjecture, left St. Petersburg to live in Sweden, writes Komsomolskaya Pravda with reference to the scientist and tutor on English language and mathematics Alexei E. Sultanov, with whom Perelman corresponded and who asked that his name not be used. Petersburg diary. Moscow's comsomolets. Grigory Perelman | In contact with
Prototypes of the Unified State Exam in mathematics 2014 with answers Here you will find prototypes of tasks in mathematics for the Unified State Exam 2014 with answers. These prototypes are from open bank tasks created by FIPI will help you pass the Unified State exam in 11th grade. Mathematics Unified State Exam Practice announcements Let's solve a math problem.
Demo version of the Unified State Exam 2014 in mathematics. Problem C2 real-gia.blogspot.ru/ Real options for State Examination in Mathematics real-gia-ege.blogspot.ru/ real option GIA 2014 in mathematics. Extracting the root B13 in Mathematics Training Unified State Exam 2014 Video tutorial Finding the volume of a parallelepiped Unified State Examination mathematics C2 rectangular parallelepiped Problems on the cube. Diagonal of the cube Unified State Examination mathematics c2. Rectangular parallelepiped Solving Problem B9 - 5 to prepare for passing the Unified State Exam 2014 Construction of sections of a parallelepiped Solution C2 mathematics 2014 Unified State Examination in mathematics. Volume of the Unified State Exam prism in mathematics. Surface area of a parallelepiped Category C2. Unified State Examination in mathematics 2014 professional Tutor Unified State Examination mathematics task C2 Angle straight plane Unified State Examination in mathematics. C2. The sphere is inscribed in a parallelepiped. Angle between straight lines Find the volume of the figure formed by rotation right triangle
