A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m if the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of water level in the tank.

Base of water tank = 11 m × 6 m

Height of water level in rectangular water tank = 5 m

Volume of water in tank = lbh = 11 m × 6 m × 5 m = 330 m³.

Let water come upto height H in cylindrical tank.

Radius = 3.5 cm

Volume of cylindrical tank = πr²H.

$\therefore πr^2H = 330 \\[1em] \Rightarrow \dfrac{22}{7} \times 3.5^2 \times H = 330 \\[1em] \Rightarrow \dfrac{22 \times 12.25 \times H}{7} = 330 \\[1em] \Rightarrow H = \dfrac{330 \times 7}{22 \times 12.25} \\[1em] \Rightarrow H = \dfrac{2310}{269.5} \\[1em] \Rightarrow H = \dfrac{60}{7} = 8\dfrac{4}{7} \text{ m}.$

Hence, the height of water level in cylindrical tank = $8\dfrac{4}{7}$ m.