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 #39 # and the height of the cylinder is #17 #. If the volume of the solid is #150 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-04-07T17:08:17

The area of the base of the cylinder is #5pi#.

The formula for volume of a cone is:
#V=pir^2h/3#

The formula for volume of a cylinder is:
#V=pir^2h#

Therefore the formula for the total volume (#V_T#) of the given solid is:

#V_T=pir^2h_1/3+pir^2h_2# (where #h_1=#height of cone, and #h_2=#height of cylinder. The radius, #r#, is the same for both.)

#V_T=pir^2(h_1/3+h_2)#

We need to calculate #r# in order to calculate the area of the base of the cylinder, hence we fill in the data given.

#150pi=pir^2(39/3+17)#

We cancel the like term (#pi#) on each side.

#150cancelpi=cancelpir^2(39/3+17)#

#150=r^2(13+17)#

#150=r^2xx30#

Divide both sides by #30#.

#150/30=r^2#

#5=r^2#

The formula of area of the base of a cylinder (a circle) is:

#A=pir^2#

#A=pixx5#

#A=5pi#