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#