Question

The curved surface area of a hemisphere is 154 cm^2. Find the volume of the hemisphere.

Answer 1

Step 1:

Given data

$\text{Curved surface area }ofhemisphere=154cm^2$

Step 2:

Write the formula for the curved surface area of the hemisphere and volume of the hemisphere.

$\begin{gathered} \text{The curved surface area = 2}\pi r^2 \\ \text{The volume of a hemisphere = }\frac{2}{3}\pi r^3 \end{gathered}$

Step 3:

To find the volume of the hemisphere, you will need to get the radius.

You can find the radius from the curved surface area of a hemisphere.

$\begin{gathered} \text{Curved surface area of hemisphere = 2}\pi r^2 \\ 154\text{ = 2 }\times\text{ }\frac{22}{7}\text{ }\times r^2 \\ 154\text{ }\times7=44r^2 \\ r^2\text{ = }\frac{154\text{ }\times\text{ 7}}{44} \\ r^2\text{ = }24.5 \\ \text{r = }\sqrt[]{24.5} \\ r\text{ = 4.95 cm} \end{gathered}$

Step 3:

$\begin{gathered} \text{Volume of the hemisphere = }\frac{2}{3}\pi r^3 \\ =\text{ }\frac{2}{3}\text{ }\times\text{ }\frac{22}{7}\text{ }\times4.95^3 \\ =254.13cm^3 \end{gathered}$