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=(4)/(3)\pi r^3`

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

`\begin{gathered} V_{}=(4)/(6)\pi r^3 \\ \text{which is equivalent to} \\ V_{}=(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=(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=(2)/(3)(3.1416)(6.5^3)`

which gives

`V=287.59cm^3`