Find the volume of the sphere if the volume of a cone with the same radius and h = 2r is 297 in^3 .

show the steps pls

1 answer

Let's start by finding the volume of the cone.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

Given that h = 2r, we can substitute this into the formula to get V = (1/3)πr^2(2r) = (2/3)πr^3.

We are given that the volume of the cone is 297 in^3, so let's set up the equation:

(2/3)πr^3 = 297

To solve for r, we can divide both sides by (2/3)π:

r^3 = 297 * (3/2) / π
r^3 = 445.5 / π
r ≈ 6.7 inches

Now we can find the volume of the sphere using the formula V = (4/3)πr^3:

V = (4/3)π(6.7)^3
V ≈ 1264.5 in^3

Therefore, the volume of the sphere is approximately 1264.5 cubic inches.