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 $243 π$ $243 pi$ , 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 $= 9 π$ $=9pi$

The volume of a cone is $V_{c} = \frac{1}{3} a h$ $V_c=1/3ah$

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

and $h =$ $h=$ height of the cone

The volume of the cylinder is $V_{l} = a \cdot H$ $V_l=a*H$

Where $H$ $H$ is the height of the cylinder

Total volume $V_{c} + V_{l} = \frac{1}{3} a h + a H = 243 π$ $V_c+V_l=1/3ah+aH=243pi$

$a (\frac{h}{3} + H) = 243 π$ $a(h/3+H)=243pi$

$a (\frac{66}{3} + 5) = 243 π$ $a(66/3+5)=243pi$

$27 a = 243 π$ $27a=243pi$

$a = \frac{243 π}{27} = 9 π$ $a=(243pi)/27=9pi$

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 6666 and the height of the cylinder is 55 . If the volume of the solid is 243π243 pi, what is the area of the base of the cylinder?