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
The formula for the volume of a cone is given by:
V = (1/3) * π * r^2 * h
where V is the volume, r is the radius of the base, and h is the height of the cone.
Given that the volume of the cone is 253π cm^3, we can rearrange the formula to solve for the height of the cone:
253π = (1/3) * π * r^2 * h
Divide both sides of the equation by π:
253 = (1/3) * r^2 * h
Now, if the height of the cone is equal to the sphere's diameter, we can substitute h with 2r (since the diameter is twice the radius):
253 = (1/3) * r^2 * 2r
Simplifying further:
253 = (2/3) * r^3
Multiply both sides of the equation by 3/2:
253 * 3/2 = r^3
379.5 = r^3
Now, if the radius of the sphere is equal to the radius of the cone (which is r), we can use the formula for the volume of the sphere:
V = (4/3) * π * r^3
Substituting r = 379.5 into the formula:
V = (4/3) * π * (379.5)^3
Calculating this expression will give you the volume of the sphere.