Question

A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.

A) determine the volume of the punch bowl to the nearest cubic centimeter.
B) If there are 1,000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.

Answer 1

The hemisphere is half the volume of a sphere. Since we are given the circumference, we can solve for the radius of the sphere. That is

`C=2\pi r`


`116\:cm=2\pi r`


`r=(116)/(2\pi )=18.462\:cm`

Part A
We can now compute for the volume of the hemisphere.

`V=(1)/(2)* (4)/(3)\pi r^3=(1)/(2)* (4)/(3)\pi \left(18.462\right)^3=13179\:cm^3`

Part B
We just need to convert the volume into its corresponding gallons

`13179\:cm^3* (1\:Liter)/(1000\:cm^3)* (1\:gallon)/(3.785\:Liters)=3.5\:gallons`