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 $66$ and the height of the cylinder is $5$ . If the volume of the solid is $243 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-11-22T19:03:50

THe area of the base of the cylinder is $=9pi$

The volume of a cone is $V_c=1/3ah$

where, $a=$ area of the base of cone and cylinder

and $h=$ height of the cone

The volume of the cylinder is $V_l=a*H$

Where $H$ is the height of the cylinder

Total volume $V_c+V_l=1/3ah+aH=243pi$

$a(h/3+H)=243pi$

$a(66/3+5)=243pi$

$27a=243pi$

$a=(243pi)/27=9pi$

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 66 66 and the height of the cylinder is 5 5 . If the volume of the solid is 243 pi243 pi, what is the area of the base of the cylinder?