Question

Cylinder A has radius 1 m and height 4 m. Cylinder B has radius 3 m and height 12 m. Find the ratio of the volume of cylinder A to the volume of cylinder B.

Answer 1

The volume ratio of Cylinder A to Cylinder B is calculated using the formula for the volume of a cylinder, resulting in a ratio of 1:27.

Step-by-step explanation:

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.

For Cylinder A, with a radius of 1 m and height of 4 m, the volume is calculated as:
V(A) = π × (1 m)² × 4 m = 4π m³.

For Cylinder B, with a radius of 3 m and height of 12 m, the volume is calculated as:
V(B) = π × (3 m)² × 12 m = 108π m³.

To find the ratio of the volume of Cylinder A to Cylinder B, we divide the volume of A by the volume of B:
Volume Ratio (A:B) = V(A) / V(B) = (4π m³) / (108π m³) = 1/27.

Therefore, the ratio of the volume of Cylinder A to Cylinder B is 1:27.

Answer 2

The fomula of a volume of a cylinder:

`V=\pi r^2H`

Cylinder A:

We have r = 1m and H = 4m. Substitute:

`V_A=\pi(1^2)(4)=\pi(1)(4)=4\pi\ m^3`

Cylinder B:

We have r = 3m and H = 12m. Substitute:

`V_B=\pi(3^2)(12)=\pi(9)(12)=108\pi\ m^3`

The ratio:

`(V_A)/(V_B)=(4\pi)/(108\pi)=(4)/(108)=(4:4)/(108:4)=(1)/(27)=1:27`