A cylindrical tank has a capacity of 6160 m³. Find its depth, if its radius is 14 m. Also, find the cost of painting its curved surface at ₹ 30 per m².

Let radius (r) = 14 m and depth or height = h meters

By formula,

Volume of cylinder = πr²h

$\Rightarrow 6160 = \dfrac{22}{7} \times 14^2 \times \text{h} \\[1em] \Rightarrow 6160 = \dfrac{22}{7} \times 196 \times \text{h} \\[1em] \Rightarrow \text{h} = \dfrac{6160 \times 7}{22 \times 196} \\[1em] \Rightarrow \text{h} = \dfrac{43120}{4312} \\[1em] \Rightarrow \text{h} = 10 \text{ m}.$

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times 14 \times 10 \\[1em] = \dfrac{6160}{7} \\[1em] = 880 \text{ m}^2$

Given, the cost of painting its curved surface is ₹ 30 per m².

⇒ 880 × 30 = ₹ 26,400.

Hence, depth of the cylindrical tank is 10 m and the cost of painting its curved surface is ₹ 26,400.