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

Answer 1

I found #8.3# units of area.

The volume of the cone is: #V_"cone"=1/3pir^2h_1# The volume of th cylinder is: #V_"cylimder"=pir^2h_2# where the "hs" are the heights of the two solids: We can write: #36pi=V_"cone"+V_"cylimder"# i.e. #36pi=1/3pir^2h_1+pir^2h_2# #36=1/3r^2*5+r^2*12# #r^2[5/3+12]=36# #r^2[41/3]=36# #r=sqrt(3/41*36)=1.6# and the area of the base will be: #A=pir^2=8.3# u.a.

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Answer 2

Theodore Abad

The area of the base of the cylinder is ( 9 \pi ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.