The earth dug out by digging a well with diam | vedclass

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(C) For the cylindrical well,the radius $r = \frac{5.4}{2} = 2.7 \, m$ and the depth $h = 20 \, m$.The volume of the earth dug out is $V = \pi r^2 h =

Vedclass · Accepted Answer

$64.8$

Vedclass · Answer

(C) For the cylindrical well,the radius $r = \frac{5.4}{2} = 2.7 \, m$ and the depth $h = 20 \, m$.The volume of the earth dug out is $V = \pi r^2 h = \pi 	imes (2.7)^2 	imes 20 \, m^3$.This earth is spread on a circular ground of radius $R = 15 \, m$ to a height $H$. The volume of this spread earth is $V = \pi R^2 H = \pi 	imes (15)^2 	imes H \, m^3$.Equating the volumes: $\pi 	imes (2.7)^2 	imes 20 = \pi 	imes (15)^2 	imes H$.$H = \frac{2.7 	imes 2.7 	imes 20}{15 	imes 15} = \frac{7.29 	imes 20}{225} = \frac{145.8}{225} = 0.648 \, m$.Converting the height to centimeters: $H = 0.648 	imes 100 = 64.8 \, cm$.Thus,the increase in the level of the ground is $64.8 \, cm$.

The earth dug out by digging a well with diameter $5.4 \, m$ and depth $20 \, m$ is uniformly spread on a circular ground with radius $15 \, m$. Find the increase in the level of the ground in $cm$.

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