A circle with a radius equal to 12 feet.

Mathematics

1 answer:

inn [45]3 years ago

8 0

Answer:

What do you mean a radius equal to 12 feet? What is your question?

Step-by-step explanation:

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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 mu

Ierofanga [76]

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

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