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 #18 # and the height of the cylinder is #36 #. If the volume of the solid is #420 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2018-04-01T13:51:29

#10pi#

Volume of cone#=pir^2h/3#

Volume of cylinder#=pi r^2h#

#:.pir^2h/3+pir^2h=420pi#

#:.pir^2*18/3+pir^2*36=420pi#

#:.pir^2(6+36)=420pi#

#:.42pir^2=420pi#

#:.42r^2=420#

#:.r^2=10#

#:.r=sqrt10#

Area of a circle#=pir^2#

#:.=pi(sqrt10)^2#

#:.=10pi#