5 cm". 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?
To find the volume of the sphere, we first need to find its radius.
Given that the height of the cone is equal to the sphere's diameter, the cone's height is twice the radius of the sphere. Since the height of the cone is 5 cm, the radius of the sphere is 5 cm ÷ 2 = 2.5 cm.
The formula for the volume of a sphere is V = (4/3) * π * r³, where V represents the volume and r represents the radius.
Plugging in the values, we get V = (4/3) * π * (2.5 cm)³.
Calculating this, we have:
V = (4/3) * 3.14 * (2.5 cm)³
= 4.19 * 15.625 cm³
= 65.26 cm³ (rounded to two decimal places)
Therefore, the volume of the sphere is approximately 65.26 cm³.