8. Find the volume of the sphere if the volume of a cone with the same radius and h = 2r is 297 in^3
To find the volume of the sphere, we first need to find the radius of the cone using the given volume.
Volume of a cone = (1/3) * π * r^2 * h
Given that the volume of the cone is 297 in^3 and h = 2r, we can substitute these values into the volume formula:
297 = (1/3) * π * r^2 * 2r
297 = (2/3) * π * r^3
r^3 = (297 * 3) / (2 * π)
r^3 = 446.5
r ≈ 7.6 inches
Now that we have found the radius of the sphere, we can calculate the volume of the sphere using the formula:
Volume of a sphere = (4/3) * π * r^3
Volume = (4/3) * π * (7.6)^3
Volume ≈ 1816.8 in^3
Therefore, the volume of the sphere is approximately 1816.8 cubic inches.