Question

Which of the following is the volume of the largest cone that can fit inside of a cube whose volume is 8 cubic inches?

(1) 2/3π in 3 (3) 7 π in 3 (2) 8/3π in 3 (4) 12 π

Answer 1

Correct option: (1)

(2/3)pi in^3

Explanation:

First we need to find the side of the cube. We know that the volume of the cube is given by the formula:

Volume = side^3

So we have that:

8 = side^3

side = 2 in

The largest cone will have its base fit in one face of the cube and the tip of the cone will touch the opposite face, so the diameter of the base and the height of the cone will be equal the side of the cube.

The volume of the cube is given by the formula:

V = (1/3) * pi * r^2 * h

With a radius = 1 in and height = 2 in, we have:

V = (1/3) * pi * 1 * 2 = (2/3)pi in3

Correct option: (1)