Question

9) A tin man has a head that is a cylinder with a cone on top. The height of the cylinder is 12 inches and the height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches. What is the volume of the tin man's head in terms of pi?

Answer 1

V of a cylinder = pi x r^2 h

V of a cone = 1/3 x pi x r^2 h

Answer 2

`\bf \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\qquad \qquad \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}\\\\ -------------------------------\\\\ \stackrel{\textit{volume of this cylinder}}{\pi (4)^2(12)}~~+~~\stackrel{\textit{volume of this cone}}{\cfrac{\pi (4)^2(6)}{3}} \\\\\\ 192\pi ~+~32\pi \implies 224\pi`