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 #12 # and the height of the cylinder is #28 #. If the volume of the solid is #36 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2018-04-20T12:13:42

#color(blue)((9pi)/8)#

Volume of a cone is given by:

#V=1/3pir^2h#

Volume of a cylinder is given by:

#V=pir^2h#

We know height of cone and cylinder:

#V=1/3pir^2(12)#

#V=pir^2(28)#

The sum of these two volumes is #36pi# given:

#:.#

#pir^2(28)+1/3pir^2(12)=36pi#

#28pir^2+4pir^2=36pi#

Factor out #r^2#:

#r^2(28pi+4pi)=36pi#

#r^2(32pi)=36pi#

#r^2=(36pi)/(32pi)=9/8#

Area of cylinder base:

#A=pir^2=pi(9/8)=(9pi)/8#