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 $9$ and the height of the cylinder is $6$ . If the volume of the solid is $45 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-05-05T14:40:46

Volume of a cone is given by $V = 1/3pir^2h$

Volume of a cylinder is given by $V = pir^2h$

$1/3pi(r)^2(9) + r^2(6)(pi) = 45pi$

$3r^2pi + 6r^2pi = 45pi$

$9r^2pi = 45pi$

$9r^2 = (45pi)/pi$

$9r^2 = 45$

$r^2 = 5$

$r = sqrt(5)$

The area of a circle is given by $r^2pi$

$(sqrt(5))^2pi$

= $5pi$

The area of the base of the cylinder is $5pi$

Hopefully this helps!

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 9 9 and the height of the cylinder is 6 6 . If the volume of the solid is 45 pi45 pi, what is the area of the base of the cylinder?