mollyb133
contestada

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.

Respuesta :

Mamasu
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 
     [tex]C=2\pi r[/tex]

     [tex]116\:cm=2\pi r[/tex]

     [tex]r=\frac{116}{2\pi }=18.462\:cm[/tex]

Part A
We can now compute for the volume of the hemisphere.
     [tex]V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3[/tex]

Part B
We just need to convert the volume into its corresponding gallons
     [tex]13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons[/tex]
Q&A Education