The volume of a cone is 253 π cm3 . 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
252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed
503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed
25 π cm3
25 pi cm cubed
256 π cm3
The correct answer is 503 π cm3.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 253 π cm3, and the height of the cone is equal to the sphere's diameter, we can solve for the radius of the cone.
253 π = (1/3)πr^2(2r)
Simplifying the equation, we get:
253 = (2/3)r^3
Dividing both sides by (2/3), we get:
r^3 = 253 * (3/2)
r^3 = 379.5
Taking the cube root of both sides, we get:
r ≈ 7.48
Now, we can find the volume of the sphere using the formula V = (4/3)πr^3.
V = (4/3)π(7.48)^3
V ≈ 503 π cm3
Therefore, the volume of the sphere is 503 π cm3.