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 #12 # and the height of the cylinder is #24 #. If the volume of the solid is #42 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2018-08-04T01:37:26

#color(maroon)("Cylinder base area " = A = 3/2 pi " sq units"#

#"Volume of cone " V_(cone) = 1/3 pi r^2 h_1#

#"Volume of cylinder " V_(cyl) = pi r^2 h_2#

#"Volume of solid " V = 1/3 pi r^2h_1 + pi r^2 h_2 = pi r^2 (1/3 h_1 + h_2)#

#"Area of cylinder base " = A = pi r^2#

#"Given " V = 42 pi, h_1 = 12, h_2 = 24, pi r^2 = ?#

#pi r^2 (1/3 h_1 + h_2) = 42 pi#

#pi r^2 = (42 pi) / (1/3 h_1 + h_2)#

#A = pi r^2 = (42 pi) / (1/3 * 12 + 24) = (42 pi) / 28#

#color(maroon)(A = 3/2 pi " sq units"#