The volume of a cone can be calculated using the formula V = 1/3 * π * r^2 * h, where r is the radius and h is the height.
Given that the volume of the cone is 253 π cm^3, we can plug in this value into the formula and solve for the radius and height:
253 π = 1/3 * π * r^2 * h
The height of the cone is equal to the sphere's diameter, which means h = 2r. Substituting this into the equation:
253 π = 1/3 * π * r^2 * 2r
253 π = 2/3 * π * r^3
To find the volume of the sphere, we can use the formula V = 4/3 * π * r^3, where r is the radius. Comparing the two formulas, we can see that the volume of the sphere is equal to 2/3 times the volume of the cone:
Volume of sphere = 2/3 * 253 π cm^3 = 169.33 π cm^3
Therefore, the volume of the sphere is 169.33 π cm^3.
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?(1 point)
1 answer