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 39 and the height of the cylinder is 17 . If the volume of the solid is 66 pi, what is the area of the base of the cylinder?

1 Answer
Yonas Yohannes
Mar 17, 2016

BA_(cyl) = pi(sqrt(11/5))^2 = 11/5pi

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Explanation:

Given: Volume cone and cylinder combined
V_(Tot) = 66pi
Heights: H_(cyl) = 17; H_("cone")=39
Required: Base Area of Cylinder, BA_(cyl)?
Solution:
V_(Tot) = 66pi = pir^2*H_(cyl)+1/3pir^2*H_("cone")
66cancel(pi) = cancel(pi)r^2*17+1/3cancel(pi)r^2*39
66 = r^2(17+13) = 30r^2; r=sqrt(11/5)

Now the base arear of the cylinder, BA_(cyl) = pir^2
BA_(cyl) = pi(sqrt(11/5))^2 = 11/5pi

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