Solid geometry Quiz 1

Question 1

The line AB cuts three parallel planes in the points A,E,B; and the line CD cuts these parallel planes in the points C,F,D. If $$AE=6	ext{ }in., \ EB=	ext{ }8	ext{ }in.,$$ and $$CD=12	ext{ }in.,$$ find CF and FD

Accepted Answer

5.14 in., 6.86 in.

Answer

5 in., 6 in

Answer

6 in., 5 in

Answer

5.34 in., 6.66 in

Question 2

A right prism of glass is  $$2\dfrac{1}{8}in.$$  Its right section is an equilateral triangle whose altitude is 0.866 in. Its lateral surface area is

Accepted Answer

6.375 sq.in

Answer

1.840 sq.in

Answer

3.680 sq.in

Answer

2.598 sq.in

Question 3

Find the volume of a prism whose height is  $$15ft$$., if each side of the triangular base is 10 in.

Accepted Answer

7794 sq.in

Answer

649.5 sq.in

Answer

150 sq.in

Answer

75 sq.in

Question 4

Consider two similar cylinders of revolution with   $$l$$ and $${l}'$$ as their lateral areas,  $$t$$ and $${t}'$$ as their total areas , $$v$$ and $${v}'$$  as their volumes ,  $$h$$ and $${h}'$$ as their altitudes  , and  $$r$$ and $${r}'$$ as their radii.  If    $$\dfrac{l}{{{l}'}}=\dfrac{{{r}^{a}}}{{{{{r}'}}^{b}}}$$ and   $$\dfrac{v}{{{v}'}}=\dfrac{{{h}^{p}}}{{{{{h}'}}^{q}}}$$ Then $$a+p = ?$$

Accepted Answer

5

Answer

4

Answer

8

Answer

6

Question 5

Consider two polar triangles  $$ABC$$ and $${A}'{B}'{C}'$$  , the letter at the vertex of each angle denoting its value in degrees , and the small letter denoting the value of the opposite side in degrees.Then, $$ \ $$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/071e4116-704a-4505-a75b-6adc694bb6168549408431509741721.png"/>

Accepted Answer

$$A+{a}'=B+{b}'=C+{c}'$$

Answer

$$A+B={a}'+{b}'=B+C={b}'+{c}'=C+A={c}'+{a}'$$

Answer

$$A=B=C$$

Answer

$${a}'={b}'={c}'$$