Mathematics: Awater reservoir is in the form of a right circular cone. the cone is 21 ft deep and has a radius of 7ft. water has collected in the cone to a depth of x ft, and has a radius of 3ft. find the volume of the water

Awater reservoir is in the form of a right circular

Ответ:

breebree6929

17.01.2022

Check the picture below.

so notice, in a cone the height and radius are always at a ratio of each other in a right-triangle, since the water level, in red, makes a similar triangle with the cone's volume, let's use proportions to get "x".

$\bf \cfrac{21}{7}=\cfrac{x}{3}\implies 3=\cfrac{x}{3}\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=3\\ h=\stackrel{x}{9} \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies \stackrel{V=27\pi }{V\approx 84.823}$