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