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 $324 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-05-16T11:11:32

Area of the base of the cylinder is $12pi$

${: (Vol_"cone",=1/3pir^2h_"cone",=22r^2pi), (ul(Vol_"cyl"),=pir^2h_"cyl",=ul(5r^2pi)), ("Total vol",,=27r^2pi) :}$

Since we are told the total volume is $324pi$
we have
$color(white)("XXX")27r^2pi=324pi$

$color(white)("XXX")rArr r^2=12$

${: (Area_"base of cyl",=r^2pi,=12pi) :}$

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 324 pi324 pi, what is the area of the base of the cylinder?