Question

A solid is made up of a hemisphere of radius x cm, and a cone of height x cm of the same radius as the hemisphere. What is the volume of the composite solid?

Answer 1

The volume of the composite solid is πx³.

Step-by-step explanation:

To find the volume of the composite solid, we need to find the volumes of the hemisphere and the cone and then add them together. The volume of the hemisphere can be found using the formula V = (2/3)πr³, where r is the radius. In this case, the radius is x, so the volume of the hemisphere is (2/3)πx³. The volume of the cone can be found using the formula V = (1/3)πr²h, where r is the radius and h is the height. In this case, both the radius and height are x, so the volume of the cone is (1/3)πx²x. Adding the volumes of the hemisphere and the cone, we get the volume of the composite solid as (2/3)πx³ + (1/3)πx²x. Simplifying this expression gives us the final answer, which is (2/3)πx³ + (1/3)πx³ = πx³.