SOLUTION: I have a punchbowl in the shape of a hemisphere with radius 9 inches. From that FULL BOWL, I am filling cylindrical glasses with the diameter of 3 inches and height of 4 inches. Ho

Question 707278: I have a punchbowl in the shape of a hemisphere with radius 9 inches. From that FULL BOWL, I am filling cylindrical glasses with the diameter of 3 inches and height of 4 inches. How many glasses can I fill? Please show or explain if can.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The volume of the punchbowl is

V = (1/2)*(4/3)*pi*r^3 ... this is half of the volume of the sphere formula

V = (1/2)*(4/3)*3.14*9^3

V = 1,526.04

So the volume of the punchbowl is approximately 1,526.04 cubic inches. So it can hold up to 1,526.04 cubic inches of liquid.

-------------------------------------------------

Volume of cylindrical glass

V = pi*r^2*h

V = 3.14*1.5^2*4 ... note: diameter = 3 --> radius = 3/2 = 1.5

V = 28.26

Each glass holds approximately 28.26 cubic inches of fluid.

So if you've completely filled the punchbowl and you want to fill each glass completely, then you will be able to fill 1526.04/28.26 = 54 glasses completely until you would need to refill the punchbowl.

Note: in the real world, you won't be able to fill something completely without spilling liquid. So keep in mind that the punchbowl will have slightly less liquid than 1526.04 cubic inches of liquid. This means that you'll have less punch to serve up. Also, each glass won't be completely filled to the top, which will allow you to fill a few more glasses because you'll have extra punch.
RELATED QUESTIONS
PLEASE HELP: A punchbowl in the hape of a hemisphere, (radius of 9 inches). We are... (answered by ankor@dixie-net.com)

A punch bowl in in the shape of a hemisphere (half of a sphere) with the radius of 8... (answered by Alan3354)

I need to calculate the volume of the top of a hemisphere at various heights of the... (answered by Alan3354)

Brad has a cylindrical barrel with radius 10 inches and height 15 inches. He wants to... (answered by Boreal)

Wine from a full cylindrical container with a diameter of 11cm and a height of 17cm is... (answered by Alan3354)

I am having trouble with my homework and need some help understanding it. Speedways... (answered by Alan3354)

A hemispherical bowl of internal bowl of radius 9 cm is full of rose water. This rose... (answered by josgarithmetic)

A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a... (answered by fractalier)

A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a... (answered by ankor@dixie-net.com)