A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $12$ and the height of the cylinder is $28$ . If the volume of the solid is $72 pi$ , what is the area of the base of the cylinder?

Question

1862 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-18T07:41:05

Area of base $= pir^2 = (9pi)/4$

enter image source here

$color(red)("Total volume = volume of cone + volume of cylinder" = 72 pi)$

volume of cone $= 1/3 pi r^2 h = 12/3pir^2 = 4*pir^2$

Volume of cylinder $= pi r^2 h = pi r^2 * 28$

Total volume $= 32pir^2 = 72 pi$

$cancelpir^2 = 72/32cancel pi=9/4$

$=>r ^2 = 9/4$

Area of base $= pir^2 = (9pi)/4$

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 12 12 and the height of the cylinder is 28 28 . If the volume of the solid is 72 pi72 pi, what is the area of the base of the cylinder?