A cone and a pyramid are both 3 inches in height. If the radius of the base of the cone is 4 in and the a side of the square base of the pyramid is 2π in, which has the larger volume? A) The cone has a larger volume by 10.79 in3. B) The pyramid has a larger volume by 10.79 in3. C) The pyramid has a larger volume by 26.91 in3. D) The cone and the pyramid have the same volume.

A) The cone has a larger volume by 10.79 in3.

Explanation:

Cone

height = 3 inches

radius = 4 inches

volume = 1/3 πr²h

volume = 1/3 × π × 4² × 3

volume = 1/3 × π × 16 × 3

volume = 1/3 × 22/7 × 48

volume = 1056 /21

volume = 50.2857142857  in³

volume = 50. 30 in³

pyramid

height = 3 inches

length of the square base  = 2π

volume = 1/3 l²h

volume  = 1/3 × (2π)² ×  3

volume = 1/3 × 4 ×  484/49 × 3

volume = 5808 /147

volume = 39.5102040816  in³

volume = 39.51 in³

Difference in volume = 50. 30 in³ - 39.51 in³ = 10.79 in³

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