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

Answer:

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

Hence $V_2=3\times V_1$

Step-by-step 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

$\frac{V_2}{V_1}=\frac{162\pi}{54\pi}$

$=3$

$\frac{V_2}{V_1}=3$

∴ $V_2=3\times V_1$

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

Answer 2

Answer:

C.3

Step-by-step explanation: