An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3 . What is the volume of the whole object

1 answer

Let's assume the radius of the hemisphere is R.

The height of the cone is equal to the diameter of the hemisphere, so it is 2R.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.

Plugging in the given values, we have 12 = (1/3)πR^2(2R).

Simplifying this equation, we get 12 = (2/3)πR^3.

To find the volume of the entire object, we need to add the volume of the hemisphere and the volume of the cone.

The volume of a hemisphere is given by the formula V = (2/3)πr^3.

Substituting R for r, we have V = (2/3)πR^3.

Therefore, the volume of the entire object is 12 + (2/3)πR^3.