A cylinder and a cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches.The cone has a radius of 3 inches.What is the height of the cone ?

Answer 1

First you need to know the Volume formulas for each shape

Volume Cone ... (1/3) pi r^2 h = V

Volume Cylinder... (pi)r^2(h) = V

Then solve for the Volume of the cylinder since we have all of the needed dimensions for this formula

(pi)2^2(3)= V

37.68 inches^3 = V (cylinder)

Now we know the volume of the Cone as well since we know that Volume Cone = Volume Cylinder

Now we will plug the Volume into the Volume Cone formula above to solve for height (h).

1/3(pi) r^2 h = V

1/3(pi)3^2 h = 37.68

1/3(pi)9h = 37.68

9.42h= 37.68 (now divide each side by 9.42 to isolate h)

h = 4 inches