Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the sphere, we first need to find the radius of the cone. We are given that the volume of the cone is 297 in^3 and that h = 2r.

The formula for the volume of a cone is V = (1/3)πr^2h. Substituting h = 2r into the formula, we get V = (1/3)πr^2(2r) = (2/3)πr^3 = 297.

Solving for r, we get r^3 = 446.25, so r ≈ 7.5 inches.

Now that we have the radius of the cone, we can find the volume of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3. Substituting r = 7.5 into the formula, we get V = (4/3)π(7.5)^3 = (4/3)π(421.875) ≈ 706.50 in^3.

Therefore, the volume of the sphere is approximately 706.50 in^3.