Question In a rain–water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.
Video Explanation
Explanatory Answer
Area of roof = 22 m × 20 m
Let the rainfall be ‘x’ m.
Volume of rain fallen on roof in m3 = area of roof × rainfall in m
= 22 × 20 × x m3
Volume of rain water collected = volume of cylindrical tank
Diameter of cylinder = 2 m. So its radius = 1 m.
Height of cylinder = 3.5 m = \\frac{7}{2}) m
Volume of rain water collected in the cylinder = π r2 h = \\frac{22}{7}) × (1)(1) × \\frac{7}{2})
Equating the two volumes.
22 × 20 × x = \\frac{22}{7}) × (1)(1) × \\frac{7}{2})
x = \\frac{1}{40}) m
Multiply by 100 to express x in cm. \\frac{1}{40}) × 100 = 2.5 cm