SOLUTION: a cone and a pyramid have equal volumes and equal heights each side of the square measures 8 meters what is the radius of the base of the cone? leave answer in terms of pi

Algebra ->  Surface-area -> SOLUTION: a cone and a pyramid have equal volumes and equal heights each side of the square measures 8 meters what is the radius of the base of the cone? leave answer in terms of pi      Log On


   

Question 281580: a cone and a pyramid have equal volumes and equal heights each side of the square measures 8 meters what is the radius of the base of the cone?
leave answer in terms of pi
Answer by Mathematicians(84) About Me  (Show Source):
You can put this solution on YOUR website!
In order to answer this question, you need to know the formula for volume of a cone and pyramid.
Volume for Cone = 1%2F3+%2A+pi+%2A+r%5E2+%2A+h where r is radius and h is height
Volume for Pyramid = 1%2F3+%2A+s%5E2+%2A+h where h is height and s is side
We know that the volumes are equal so we get:
1%2F3+%2A+pi+%2A+r%5E2+%2A+h+=+1%2F3+%2A+s%5E2+%2A+h multiplying 3
+pi+%2A+r%5E2+%2A+h+=+s%5E2+%2A+h since h is the same, we can cancel them out
+pi+%2A+r%5E2+=+s%5E2 We are given that side is 8
+pi+%2A+r%5E2+=+64 some algebra
+r%5E2+=+64%2Fpi+
+r+=+8%2F%28pi%29%5E%281%2F2%29 you would also have a negative answer, however since we are dealing with distance, we only consider the positive answer.
I hope this helps,
Bran ;)