SOLUTION: A cylinder has a surface area of 72pi square centimeters and a height of 5 centimeters. The volume of the cylinder is equal to ______pi cubic centimeters.

Algebra ->  Test -> SOLUTION: A cylinder has a surface area of 72pi square centimeters and a height of 5 centimeters. The volume of the cylinder is equal to ______pi cubic centimeters.      Log On


   

Question 1197274: A cylinder has a surface area of 72pi square centimeters and a height of 5 centimeters. The volume of the cylinder is equal to ______pi cubic centimeters.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
A cylinder has a surface area of 72pi square centimeters and a height of 5 centimeters.
The volume of the cylinder is equal to ______pi cubic centimeters.
~~~~~~~~~~~~~~~


I don't like the " problems " that come with the blank, which I should fill.

I don't like when other people communicate with me this way.

They simply do not respect a reader.


A professionally written source will never present a problem in this way.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The general formula for the total surface area of a cylinder is:
TSA=+2pi%2Ar%5E2+%2B2+pi%2Ar%2Ah
given:
TSA=72cm%5E2
+h=5cm
then
2pi%2Ar%5E2+%2B2pi%2Ar%2A5=72pi....divide by pi
2r%5E2+%2B10r=72
2r%5E2+%2B10r-72=0...divide by+2
r%5E2+%2B5r-36=0..........factor and find r
%28r+-+4%29+%28r+%2B+9%29+=+0
take only positive solution:
r=4cm

A cylinder's volume is:
V=pi%2Ar%5E2%2Ah............substitute r and+h
V=pi%2A%284cm%29%5E2%2A5cm
V=pi%2A16cm%5E2%2A5cm
V=pi%2A80cm%5E3=> exact solution
V=251.33cm%5E3=> approximately

answer:
The volume of the cylinder is equal to 80pi cubic centimeters.