High School

What is the capacity of a bucket that is 42 cm deep, and the inner radii of the base and the topmost part of the bucket are 12 cm and 20 cm, respectively?

A. 22,176 cm³
B. 34,188 cm³
C. 45,120 cm³
D. 58,572 cm³

Answer :

Final answer:

The capacity of the bucket is 22,176 cm³.

Explanation:

To find the capacity of the bucket, we need to calculate the volume of the frustum of the cone. The formula to calculate the volume of a frustum of a cone is given by:

V = (1/3)πh(R1² + R2² + R1R2)

Substituting the given values, we can calculate the capacity of the bucket:

V = (1/3)π(42 cm)(12 cm² + 20 cm² + 12 cm * 20 cm)

V = (1/3)π(42 cm)(144 cm² + 400 cm² + 240 cm²)

V = (1/3)π(42 cm)(784 cm²)

V ≈ 22,176 cm³

Therefore, the correct answer is a) 22,176 cm³.

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