If a solid cone of volume 27, pi, cm^3 is kep | vedclass

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(C) Let the radius and height of the cone be $r$ and $h$ respectively.The volume of the cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h = 27\, \pi\

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(C) Let the radius and height of the cone be $r$ and $h$ respectively.The volume of the cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h = 27\, \pi\, cm^3$.The volume of the cylinder with the same radius $r$ and height $h$ is $V_{cylinder} = \pi r^2 h$.The empty space inside the cylinder after placing the cone is the difference between the volume of the cylinder and the volume of the cone.Volume of empty space $= V_{cylinder} - V_{cone} = \pi r^2 h - \frac{1}{3} \pi r^2 h = \frac{2}{3} \pi r^2 h$.Since $\frac{1}{3} \pi r^2 h = 27\, \pi$,we have $\pi r^2 h = 3 	imes 27\, \pi = 81\, \pi$.Therefore,the volume of water needed $= 81\, \pi - 27\, \pi = 54\, \pi\, cm^3$.

If a solid cone of volume $27\, \pi\, cm^3$ is kept inside a hollow cylinder whose radius and height are the same as that of the cone,then the volume of water needed to fill the empty space is...........$\pi\, cm^3$.

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