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 18 and the height of the cylinder is 36 . If the volume of the solid is 420 pi, what is the area of the base of the cylinder?

1 Answer
Jul 30, 2018

color(green)("radius of the cone " = r = sqrt 10, " units"

Explanation:

https://socratic.org/questions/a-solid-consists-of-a-cone-on-top-of-a-cylinder-with-a-radius-equal-to-that-of-t-85

"Given " h_1 = 18, h_2 = 36, V = 420 pi

"Volume of the solid " = V = V_(cone) + V_(cyl)

V_(cone) = 1/3 pi r^2 h = 1/3 pi r^2 18 = 6 pi r^2

V_(cyl) = pi r^2 h = pi r^2 36 = 36 pi r^2

V = 6 pi r^2 + 36 pi r^2 = 420 pi

42 pi r^2 = 420 pi

r^2 = cancel(420 pi)^color(red)(10) / cancel(42 pi) = 10

color(green)("radius of the cone " = r = sqrt 10, " units"