What is the area of the base of a cylinder with a volume of 174π in.3 and a height of 12 inches? 1. Apply the formula for the volume of a cylinder: V = Bh

2. Substitute the known measures into the formula: 174π = B(12)

3. Apply the division property of equality:
174π
12
= B
12
12

The area of the base of the cyclinder is
π in.2.

14.5 in²

Explanation:

A cylinder is the locus of a line moving parallel to the axis and at a fixed distance from the axis.

The volume of a cylinder (V) is:

V = πr²h, where h is the cylinder height, r is the radius of the base.

But The base area (B) = πr², hence

V = Bh

Given that height (h) = 12 inches, volume (V) = 174π in³, the base area us gotten using:

V = Bh

174π = B(12)

Dividing both sides by 12:

174π / 12 = B(12) / 12

B = 14.5π in²

Hence the area of the base of the cylinder is 14.5 in²

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