Find the volume of the sphere if the volume of a cone with the same radius and h = 2r is 297 in^3 .
Let V_cone be the volume of the cone and V_sphere be the volume of the sphere.
Given that the volume of the cone is V_cone = (1/3) * π * r^2 * h = 297 in^3, and h = 2r, we can rewrite the volume of the cone as:
V_cone = (1/3) * π * r^2 * 2r = 2/3 * π * r^3
We know that V_cone = 297 in^3, so we have:
2/3 * π * r^3 = 297
Now, solve for r:
r^3 = (297 * 3) / (2 * π) = 445.5 / π
r = (445.5 / π)^(1/3)
The volume of a sphere is given by V_sphere = (4/3) * π * r^3, so substitute the value of r in:
V_sphere = (4/3) * π * (445.5 / π)^(1/3)
V_sphere ≈ 1427.63 in^3
Therefore, the volume of the sphere is approximately 1427.63 cubic inches.