Mathematics

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

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Given,

Tank's diameter = 2 m

Tank's radius (r) = $\dfrac{2}{2}$ = 1 m

Width of embarkment (w) = 2 m

External radius (R) = r + w = 1 + 2 = 3 m.

Height of embarkment (h) = 1.6 m

Let depth of tank be h' meters.

Volume of earth removed = Volume of embarkment formed

⇒ πr²h' = π(R² - r²)h

⇒ 1²h' = (3² - 1²) × 1.6

⇒ h' = (9 - 1) × 1.6 m

⇒ h' = 12.8 m

Hence, depth of circular tank = 12.8 m.

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