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 #135 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-09-16T08:58:13

#15pi#

Cone volume #(1/3)pir^2(h_1) = (1/3)pir^2(9)=3pir^2#

Cylinder volume #=pir^2(h_2)=pir^2xx6=6pir^2#

solid volume = cone volume + cylinder volume

#=> 135pi = 3pir^2+6pir^2=9pir^2#

#=> r^2=135/9 =15#

cylinder base area #= pir^2 = 15pi#

Solution 2)

As the cone and the cylinder have the same radius, they have the same base area.

Let #A_(base)# be the base area

Cone volume #1/3A_(base)h_1=1/3A_(base)xx9=3A_(base)#

Cylinder volume #A_(base)h_2=6A_(base)#

solid volume = cone volume +cylinder volume

#=> 135pi=3A_(base)+6A_(base)=9A_(base)#
#=> A_(base) = (135pi)/9=15pi#