Question

A conical tank has an inside diameter of 20 ft and a height of 12 ft. The tank is filled with liquid to a height of 9 ft. How much liquid is in the tank? (Round your answer to the nearest whole number.)

Answer 1

check the picture below

so.. if you notice, the diameter is 20, the radius is half that, the radius and height are at a ratio of 5:6, if the larger cone is filled up to 9ft, that means, the conical gap above, is 3ft in height

so, simply getting the volume of the larger cone filled up, with a height of 12, and then subtracting that conical gap, you'd end up with what's leftover, whatever the volume is at 9ft


`\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\\\\ -------------------------------\\\\ \textit{volume of larger cone}\qquad V_l=\cfrac{\pi 10^2\cdot 12}{3}\implies \boxed{V_l=400\pi } \\\\\\ \textit{volume of smaller cone}\qquad V_s=\cfrac{\pi \left( (5)/(2) \right)^2\cdot 3}{3}\implies \boxed{V_s=\cfrac{25\pi }{4}} \\\\\\ \textit{volume of liquid up to 9ft}\qquad V_l-V_s=\cfrac{1575\pi }{4}\implies 393.75\pi`