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

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Answer 1 · 2018-01-08T07:31:33

Area of base of the cylinder #A_b = (3pi)/4 = color (red)(2.3562)#

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Volume of solid #V_s# = vol. of cylinder + vol. of cone

Given #V_s = 12pi, h_(cyl) = 5, h_(co) = 33#

#V_s = 12pi = (pi r^2 h_(cyl) + (1/3) pi r^2 h_(co))#

# 12pi = pi r^2(5 + (1/3)33) = 16 pi r^2#

#r^2 = (12 pi) / (16 pi) = (3/4)#

# Area of base A_b = pi r^2 = pi * (3/4) = 2.3562#