Question

The height of one right circular cylinder is 6 centimeters and its radius is 3 centimeters. The height of a second right circular cylinder is 18 centimeters and its radius is 3 centimeters. The volume of the second cylinder is how many times as large as the volume of the first cylinder?

A. 12

B. 4

C. 3

D. 2

Answer 1

C.3

Explanation:

Answer 2

The volume of the second cylinder is three times as large as the volume of the first cylinder .

Hence
`V_2=3* V_1`

Explanation:

Given that the height of one right circular cylinder is 6 centimeters and its radius is 3 centimeters.

Let
`h_1,r_1` be the height and radius of the first right circular cylinder respectively.

∴
`h_1=6 cm` and
`r_1=3 cm`

The height of a second right circular cylinder is 18 centimeters and its radius is 3 centimeters.

Let
`h_2,r_2` be the height and radius of the second right circular cylinder respectively.

∴
`h_1=18 cm` and
`r_1=3 cm`

To find the volume of the second cylinder is how many times as large as the volume of the first cylinder :

The formula for Volume of right circular cylinder is

`V=\pi r^2h` units

The Volume of first right circular cylinder is

`V_1=\pi r_1^2h_1`

Substitute the values in the formula we get

`V_1=\pi (3^2)(6)`

`V_1=\pi (9)(6)`

`=54\pi` units

∴
`V_1=54\pi` units

The Volume of second right circular cylinder is

`V_2=\pi r_2^2h_2`

Substitute the values in the formula we get

`V_2=\pi (3^2)(18)`

`V_2=\pi (9)(18)`

`=162\pi` units

∴
`V_2=162\pi` units

From the volumes
`V_1 and V_2` we get

`(V_2)/(V_1)=(162\pi)/(54\pi)`

`=3`

`(V_2)/(V_1)=3`

∴
`V_2=3* V_1`

The volume of the second cylinder is three times as large as the volume of the first cylinder .