SOLUTION: A cone and a pyramid are both 3 inches in height. If the radius of the base of the cone is 4 in and the a side of the square base of the pyramid is 2π in, which has the larger vol

Algebra ->  Volume -> SOLUTION: A cone and a pyramid are both 3 inches in height. If the radius of the base of the cone is 4 in and the a side of the square base of the pyramid is 2π in, which has the larger vol      Log On


   

Question 1135666: A cone and a pyramid are both 3 inches in height. If the radius of the base of the cone is 4 in and the a side of the square base of the pyramid is 2π in, which has the larger volume?
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


Cone: V = (1/3)(pi)(r^2)(h) = (1/3)(pi)(4^2)(3) = 16(pi)

Square pyramid: V = (1/3)(B)(h) = (1/3)(2pi)^2(3) = 4(pi)^2

To see which is greater, divide each expression by their common factor 4(pi):

Cone: (16(pi))/(4(pi)) = 4
Pyramid: 4(pi)^2/(4(pi)) = (pi)