Question

What is the volume of the figure below? The top of the hemisphere in the bottom of a cylinder

Answer 1

We can calculate the volume of this figure by adding the volume of the hemisphere and the cylinder.

The hemisphere will have a volume that is half of the volume of a sphere with radius 10 in.

The cylinder will have a volume that is the area of the base, a circle of radius 10 in., times the height h = 16 in.

We then can express the volume of the figure as:

`\begin{gathered} V=V_h+V_c \\ V=(1)/(2)\cdot(4)/(3)\pi r^3+\pi r^2h \\ V=(2)/(3)\pi\cdot10^3+\pi\cdot10^2\cdot16 \\ V=(2000)/(3)\pi+1600\pi \\ V=(2000+3*1600)/(3)\pi \\ V=(6800)/(3)\pi \\ V\approx7120.9 \end{gathered}`

Answer: the volume is approximately 7120.9 cubic inches.