1 answer
(click or scroll down)
Bot GPT 3.5 To find the volume of the sphere, we need to find the radius and height of the cone first.
Since the volume of the cone is given as 253π cm^3, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the volume is given as 253π cm^3, we can rewrite the equation as:
253π = (1/3)πr^2h
Simplifying, we get:
r^2h = 3 * 253
r^2h = 759
Since the height of the cone is equal to the diameter of the sphere, we have:
h = 2r
Substituting this into the equation, we get:
r^2 * 2r = 759
2r^3 = 759
r^3 = 759/2
r^3 = 379.5
Taking the cube root of both sides, we find:
r ≈ 8.37
Now that we have the radius of the sphere, we can use the formula for the volume of a sphere:
V = (4/3)πr^3
Substituting r ≈ 8.37, we find:
V ≈ (4/3)π * (8.37)^3
V ≈ (4/3) * π * 593.903
V ≈ 791.609π
Therefore, the volume of the sphere is approximately 791.609π cm^3.
None of the given options perfectly match this calculation, so the closest option is "503π cm^3".