Question

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 the water level in the tank.

Answer 1

Volume of water in tank = Volume of cuboidal tank up to a height of 5 m

According to the question,

For cuboidal tank

Length, l = 11 m

Breadth, b = 6 m

Height, h = 5 m

We know that the equation to find the volume of the tank,

Volume of tank = lbh, where, l, b and h are the length, breadth and height of tank respectively

Volume of water = 11(6)(5) = 330 m³

We also know that,

Base radius of cylindrical tank, r = 3.5 m

Let the height till which the cylindrical tank is filled = h m

Hence, using the formula,

Volume of a cylinder = πr²h, where r is base radius and h is the height of cylinder

Volume of water in cylindrical tank = π(3.5)²h

330 m³ = `22/7 xx 3.5 xx 3.5 xx "h"`

330 m³ = h × 38.5

h = 8.57 m

Hence, the height till which the cylindrical tank is filled = 8.57 m