Question

What is the volume of a hemisphere with radius 3 ft? What is the volume of a hemisphere with diameter 13 cm?

Answer 1

The volume of a sphere is given by

$V_s=\frac{4}{3}\pi r^3$

Since a hemisphere is half sphere, its volume is given by

$\begin{gathered} V_{}=\frac{4}{6}\pi r^3 \\ \text{which is equivalent to} \\ V_{}=\frac{2}{3}\pi r^3 \end{gathered}$

where r is the radius.

Case a.

In this part r=3 ft, then by substituting this values into our last formula we get

$V=\frac{2}{3}(3.1416)(3^3)$

which gives

$V=56.55ft^3$

Case b.

In this part r=(13/2) cm, then by substituting this values into our last formula we get

$V=\frac{2}{3}(3.1416)(6.5^3)$

which gives

$V=287.59cm^3$