SOLUTION: Good afternoon!I need some help with a problem so can somebody help me? In cubic feet, how much greater is the volume of a cone with a height of 10 ft and the radius 6 ft than t

Algebra ->  Volume -> SOLUTION: Good afternoon!I need some help with a problem so can somebody help me? In cubic feet, how much greater is the volume of a cone with a height of 10 ft and the radius 6 ft than t      Log On


   

Question 139864: Good afternoon!I need some help with a problem so can somebody help me?
In cubic feet, how much greater is the volume of a cone with a height of 10 ft and the radius 6 ft than the volume of a square pyramid with a height of 10 ft and base edge length of 6 ft.
That is my question thanks so much whoever answers this!
Sincerely Confuse Student!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to find the volume of the cone and that of the square pyramid.
Volume of the cone, V%5Bc%5D:
V%5Bc%5D+=+%281%2F3%29%28pi%29r%5E2h where: r = 6 ft., h = 10 ft., and pi+=+3.14approx. Making the appropriate substitutions:
V%5Bc%5D+=+%281%2F3%29%283.14%29%286%29%5E2%2810%29
V%5Bc%5D+=+%281%2F3%29%283.14%29%2836%29%2810%29
V%5Bc%5D+=+%281%2F3%29%283.14%29%28360%29
V%5Bc%5D+=+376.8 Cu.ft.
Volume of square pyramid, V%5Bp%5D:
V%5Bp%5D+=+%281%2F3%29Bh where: B = area of the square base (36sq.ft), h = height (10ft.). Making the appropriate substitution:
V%5Bp%5D+=+%281%2F3%29%2836%29%2810%29
V%5Bp%5D+=+120 Cu.ft.
Find the difference of the two volumes:
V%5Bc%5D+-+V%5Bp%5D+=+376.8-120
V%5Bc%5D+-+V%5Bp%5D+=+256.8 Cu.ft.
The volume of the cone is 256.8 Cu.ft greater than the volume of the square pyramid.