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 $33$ and the height of the cylinder is $14$ . If the volume of the solid is $225 pi$ , what is the area of the base of the cylinder?

Question

1540 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-04T10:44:53

$(75pi)/13$

Assume the radius of the cylinder/cone as r, height of cone as $h_1$ , height of cylinder as $h_2$

Volume of the cone part of solid = $(pi*r^2*h_1)/3$

Volume of the cylinder part of solid = $pi*r^2 * h_2$

What we have is:

$h_1$ = 33, $h_2$ = 14

$(pi*r^2*h_1)/3$ + $pi*r^2 * h_2$ = $225*pi$

$(pi*r^2*33)/3$ + $pi*r^2 * 14$ = $225*pi$

$pi*r^2 * 11$ + $pi*r^2 * 28$ = $225*pi$

$39.pi*r^2$ = $225*pi$

$r^2$ = $225/39$ = $75/13$

Area of the base of the cylinder = $pi*r^2$ = $pi*75/13$ = $(75pi)/13$

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 33 33 and the height of the cylinder is 14 14 . If the volume of the solid is 225 pi225 pi, what is the area of the base of the cylinder?