SOLUTION: Hi Free Tutors! Here is my problem: A hole is 33 feet deep and 3 feet in circumference. How many yards of concrete will it take to fill it? Thanks! NR

Algebra ->  Volume -> SOLUTION: Hi Free Tutors! Here is my problem: A hole is 33 feet deep and 3 feet in circumference. How many yards of concrete will it take to fill it? Thanks! NR      Log On


   

Question 74681: Hi Free Tutors!
Here is my problem:
A hole is 33 feet deep and 3 feet in circumference. How many yards of concrete will it take to fill it?
Thanks!
NR
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to find the radius. We can use the circumference formula to find r:
C=2%2Api%2Ar
Plug in C=3 and solve for r
3=2%2Api%2Ar
r=0.4775

Now use the volume of a cylinder formula:
V=pi%2Ar%5E2h
Plug in r=0.4775 and h=33 to find V
V=pi%2A%280.4775%29%5E2%2833%29
V=23.638
This means it will take 23.638 ft%5E3 (cubic feet) to fill the hole. We must convert to cubic yards:
1 cubic foot=1/27 cubic yards

23.638cross%28ft%5E3%29%2A%281%2F27%29%28yrd%5E3%2Fcross%28ft%5E3%29%29=0.875481
So the hole is 0.875481 cubic yards and it will take the same amount of concrete to fill it.