12,572 views
22 votes
22 votes
The curved surface area of a hemisphere is 154 cm^2. Find the volume of the hemisphere.

User SHT
by
2.5k points

1 Answer

11 votes
11 votes

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 = }(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 }*\text{ }(22)/(7)\text{ }* r^2 \\ 154\text{ }*7=44r^2 \\ r^2\text{ = }\frac{154\text{ }*\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 = }(2)/(3)\pi r^3 \\ =\text{ }(2)/(3)\text{ }*\text{ }(22)/(7)\text{ }*4.95^3 \\ =254.13cm^3 \end{gathered}

User CoMartel
by
3.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.