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Earth dug out of on making a circular tank of radius 3.5m is spread all around the tank uniformly to a width of 1m to form an embankment of height 7m then find depth of the tank is

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\frac{31}{7}

31 m

\frac{32}{7}

32 m

answer is C.

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Detailed Solution

r = 3.5 m

$R = 3.5 + 1 = 4.5 m$

Volume of embankment $= π (R + r) (R - r) h$

$= π (8) \times 1 \times 7 m^{3}$

Volume of earth dug out $= 56 π m^{3}$

$π \times {(3.5)}^{2} \times h_{1} = 56 π$

$h_{1} = \frac{56}{12.25} = \frac{56}{12 \frac{1}{4}} = \frac{56 \times 4}{49} = \frac{32}{7}$ m

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