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)
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height.
Given that the volume of the cone is 25/3 π cm^3, we can express this as:
25/3 π = (1/3)πr^2h
Since the height of the cone is equal to the diameter of the sphere, we have h = 2r.
Substitute h = 2r into the volume formula for the cone:
25/3 π = (1/3)πr^2(2r)
25/3 = 2r^3
r^3 = 25/6
r = (25/6)^(1/3)
Now, the volume of a sphere is given by the formula V = (4/3)πr^3. Given that the radius of the sphere is the same as the cone's, we can substitute r = (25/6)^(1/3) into the volume formula for the sphere:
V_sphere = (4/3)π(25/6)^(1/3)^3
V_sphere = (4/3)π(25/6)
V_sphere = 100/18 π
V_sphere = 50/9 π
Therefore, the volume of the sphere is 50/9 π cm^3.
no , pls try again
Sorry about that mistake. Let's try again.
Given that the volume of the cone is 25/3 π cm^3, we have:
V_cone = 25/3 π = (1/3)πr^2h
Since the height of the cone is equal to the diameter of the sphere, we have h = 2r.
Substitute h = 2r into the volume formula for the cone:
25/3 = (1/3)πr^2(2r)
25 = 2r^3
r^3 = 25/2
r = (25/2)^(1/3)
Now, the volume of a sphere is given by the formula V = (4/3)πr^3. Given that the radius of the sphere is the same as the cone's, we can substitute r = (25/2)^(1/3) into the volume formula for the sphere:
V_sphere = (4/3)π((25/2)^(1/3))^3
V_sphere = (4/3)π(25/2)
V_sphere = (100/6)π
V_sphere = 50/3 π
Therefore, the volume of the sphere is 50/3 π cm^3.