The volume of a cone is 25/3 π cm^3 . What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
Responses
25/6 π cm3
50/3 π cm3
25 π cm3
25/2 π cm3
First, we can find the radius of the cone by using the formula for the volume of a cone:
V = (1/3)πr^2h
25/3π = (1/3)πr^2h
25/3π = (1/3)πr^2(h/2) [since the height of the cone is equal to the sphere's diameter]
25/3 = (1/3)r^2
r^2 = 25
r = 5
Since the radius of the sphere is also 5 (same as the cone), we can find the volume of the sphere using the formula:
V = (4/3)πr^3
V = (4/3)π(5)^3
V = (4/3)π(125)
V = (4/3)(125)π
V = 500/3π
Therefore, the volume of the sphere is 500/3π, which is equivalent to 166.67π or approximately 523.6 cm^3.
So, the correct response is:
50/3 π cm3