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 #66 # and the height of the cylinder is #5 #. If the volume of the solid is #243 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2016-11-22T19:03:50

THe area of the base of the cylinder is #=9pi#

The volume of a cone is #V_c=1/3ah#

where, #a=# area of the base of cone and cylinder

and #h=# height of the cone

The volume of the cylinder is #V_l=a*H#

Where #H# is the height of the cylinder

Total volume #V_c+V_l=1/3ah+aH=243pi#

#a(h/3+H)=243pi#

#a(66/3+5)=243pi#

#27a=243pi#

#a=(243pi)/27=9pi#