Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.