A well with radius 2 , m and depth 50 , m is | vedclass

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(B) The volume of the soil taken out from the well is equal to the volume of the cylinder formed by the well.Volume of soil = $\pi r^2 h = \pi 	imes

Vedclass · Accepted Answer

$12.5$

Vedclass · Answer

(B) The volume of the soil taken out from the well is equal to the volume of the cylinder formed by the well.Volume of soil = $\pi r^2 h = \pi 	imes (2)^2 	imes 50 = 200\pi \, m^3$.Let the increase in the level of the circular plot be $H$ meters.The soil is spread over a circular plot of radius $R = 40 \, m$.The volume of the soil spread is equal to the volume of the cylinder of radius $40 \, m$ and height $H$.Volume = $\pi R^2 H = \pi 	imes (40)^2 	imes H = 1600\pi H \, m^3$.Equating the two volumes: $1600\pi H = 200\pi$.$H = \frac{200}{1600} = \frac{1}{8} \, m$.To convert the height into $cm$,multiply by $100$: $H = \frac{1}{8} 	imes 100 = 12.5 \, cm$.

$A$ well with radius $2 \, m$ and depth $50 \, m$ is dug and the soil taken out is spread evenly on a circular plot with radius $40 \, m$. Find the increase in the level of the plot in $cm$.

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