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 $36$ and the height of the cylinder is $6$ . If the volume of the solid is $48 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-03-23T00:56:43

$A=2.667pi$

$A = 8.37$

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We can use the volume of the shape to solve for the radius using the combination of the volume of the cylinder and the cone.

Volume of a Cone = $1/3pir^2h$
Volume of a Cylinder = $pir^2h$

Total Volume = $1/3pir^2h+pir^2h$

$48pi = 1/3pir^2(36)+pir^2(6)$

$48pi = 12pir^2+6pir^2$

$48pi = 18pir^2$

$(48cancelpi)/(18cancelpi) = ((cancel18cancelpi)r^2)/(cancel18cancelpi)$

$2.667 = r^2$

$sqrt2.667 = sqrt(r^2)$

$1.633 = r$

Area of the circular base is $A=pir^2$

$A=pi(1.633)^2$

$A=2.667pi$

$A = 8.37$

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 36 36 and the height of the cylinder is 6 6 . If the volume of the solid is 48 pi48 pi, what is the area of the base of the cylinder?