Question

The volume of a cone is 25/3 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

a. 25/6 π cm3

Start Fraction 25 over 6 End Fraction pi cm cubed

b. 50/3 π cm3

Start Fraction 50 over 3 End Fraction pi cm cubed

c. 25/2 π cm3

Start Fraction 25 over 2 End Fraction pi cm cubed

25 π cm3

Answer 1

Let r be the common radius. The cone's height h = 2r. So
V_cone = (1/3)π r^2 h = (1/3)π r^2(2r) = (2/3)π r^3 = 25/3 π.
Thus 2 r^3 = 25 ⇒ r^3 = 25/2.
The sphere's volume is V_sphere = (4/3)π r^3 = (4/3)π (25/2) = (50/3)π cm^3.

Answer: b. 50/3 π cm^3.