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 #33 # and the height of the cylinder is #17 #. If the volume of the solid is #140 pi#, what is the area of the base of the cylinder?

Answer 1

#S=5pi#

The volume of a cylinder #V# is #V=Sh#, where #S# is the area of the base and #h# is the height. The volume of a cone is #V=1/3Sh#.

Let #S# the area of the base in this solid. The volume of the cone is #V_"co"=1/3*S*33=11S# and the volume of the cylinder is #V_"cy"=S*17=17S#

The total volume is #V=V_"co"+V_"cy"=11S+17S=28S#. Therefore, #28S=140pi# #S=5pi# is the required answer.

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Answer 2

Claire Akin

The area of the base of the cylinder is ( 49\pi ) square units.

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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.