What is the ratio of the volume of cylinder A, which has a radius of 1 meter and a height of 4 meters, to the volume of cylinder B, which has a radius of 2 meters and the same height of 4 meters?

To find the ratio of the volumes of two cylinders, we can use the formula for the volume V of a cylinder, which is given by:

V = πr²h

Where:

• r = radius of the cylinder
• h = height of the cylinder
• π ≈ 3.14 (or you can use the greater precision of π as needed)

Now, let’s calculate the volumes of both cylinders:

Volume of Cylinder A

For Cylinder A:

• Radius (r_A) = 1 m
• Height (h_A) = 4 m

Using the volume formula:

V_A = π(1 m)²(4 m)

V_A = π(1)(4)

V_A = 4π m³

Volume of Cylinder B

For Cylinder B:

• Radius (r_B) = 2 m
• Height (h_B) = 4 m

Using the volume formula:

V_B = π(2 m)²(4 m)

V_B = π(4)(4)

V_B = 16π m³

Finding the Ratio

Now, we need to find the ratio of the volume of Cylinder A to the volume of Cylinder B:

Ratio = V_A : V_B

Ratio = (4π m³) : (16π m³)

The π in the numerator and denominator cancel out:

Ratio = 4 : 16

Simplifying that ratio gives:

Ratio = 1 : 4

This means that the volume of Cylinder A is one-fourth the volume of Cylinder B.