Question

A cylinder and a rectangular prism have the same volume and same height. The base of the prism is a square with side length 9 cm.



What is the approximate radius of the cylinder?



A.
4.5 cm


B.
5.1 cm


C.
12.9 cm


D.
25.8 cm

Answer 1

If they have both the same volume and the same height, then they must also have the same area (base.)

Answer 2

This is because the volume of a cylinder or prism is the area of the base times the height.

Answer 3

The area of a square is the side length, squared.

Answer 4

b

Answer 5

So the area of the square base of the rectangular prism is 81 cm^2.

Answer 6

The area of a circle is pi * radius^2.

Answer 7

pi*radius^2=81
radius^2=81/pi
radius=sqrt(81/pi).

Answer 8

This is approximately 5.07770625193. So the answer, indeed, is (B).

Answer 9

A cylindrical can of baked beans has a diameter of 8 cm and a height of 9 cm.

What is the exact volume of the can?



A.


72π cm³


B.


144π cm³


C.


648π cm³


D.


2304π cm³

Answer 10

The volume of a cylinder is the area times the height. The area of a circle is the radius squared times pi.

Answer 11

If the diameter is 8, then the radius is 4.

Answer 12

4^2=16

Answer 13

The area of the circular base is pi*16.

Answer 14

The height is 9, so pi*16*9=144pi.

Answer 15

The answer is (B).

Answer 16

Do you need any more help?