SOLUTION: PLEASE HELP: A punchbowl in the hape of a hemisphere, (radius of 9 inches). We are filling from that FULL bowl cylindrical glasses with a diameter of 3 inches and height of 4 in

Algebra ->  Volume -> SOLUTION: PLEASE HELP: A punchbowl in the hape of a hemisphere, (radius of 9 inches). We are filling from that FULL bowl cylindrical glasses with a diameter of 3 inches and height of 4 in      Log On


   

Question 707267: PLEASE HELP:
A punchbowl in the hape of a hemisphere, (radius of 9 inches). We are filling from that FULL bowl cylindrical glasses with a diameter of 3 inches and height of 4 inches.How many glasses can we fill? Please show or explain so I can understand as I have several problems of the like.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A punchbowl in the shape of a hemisphere, (radius of 9 inches).
We are filling from that FULL bowl cylindrical glasses with a diameter of 3 inches and height of 4 inches.
How many glasses can we fill?
:
We want to find the volume of the liquid in the full bowl, then the volume of the liquid in the glass.
Divide the vol in the bowl by the vol in the glass, to get the number of glasses
:
Vol of a half sphere: V = 1%2F2*4%2F3*pi%2Ar%5E3
V = 4%2F6*pi%2A9%5E3
V = 1526.8 cu/inches in the bowl
:
Vol of a cylinder: V = pi%2Ar%5E2%2Ah
Radius of the glass; 3/2 = 1.5 inches
V = pi%2A1.5%5E2%2A4
V = 28.3 cu/inches in each glass
:
Find the number of glasses
1526.8%2F28.3 = 53.9 ~ 54 glasses can be filled
:
:
This is the method, be sure and check my math here.