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 $24$ and the height of the cylinder is $4$ . If the volume of the solid is $90 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2017-12-28T01:19:25

Base Area $= 23.56$

Combine the equations for the volumes of the cylinder and the cone to find the radius. Then calculate the base area ( $pir^2$ ).

$V_"cone" = 1/3pir^2h$
$V_"cyl" = pir^2h$

$V = 90pi = 1/3pir^2h + pir^2h$

$90 = 1/3r^2xx24 + r^2xx4 = 12r^2$
$r^2 = 7.5$

Because we want $r^2$ for the area anyway, we do not need to go further.
Base Area = $pir^2 = pixx7.5 = 23.56$

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 24 24 and the height of the cylinder is 4 4 . If the volume of the solid is 90 pi90 pi, what is the area of the base of the cylinder?