In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep
Solution:
Since there was a rainfall of 10 cm in a river valley of area 7280 km², the volume of the rainfall will be calculated as follows:
Volume of the rainfall = Area of the river valley × height of rainfall in the river valley
Volume of the river = length × breadth × height [Assuming the river valley to be cuboidal]
Area of the valley, A = 7280 km² = 7280 × 1000000 m² = 7.28 × 109 m²
Height of rainfall in a fortnight, h = 10 cm = 10/100 m = 0.1 m
Volume of the rainfall = Area of the river valley × height of rainfall in the river valley
= 7.28 × 109 m² × 0.1 m
= 7.28 × 108 m³
Length of river, l = 1072 km = 1072 × 1000 m = 1.072 × 106 m
Width of river, b = 75 m
Depth of river, h = 3 m
Volume of 3 rivers = 3 × volume of one river
= 3 lbh
= 3 × 1.072 × 106 m × 75 m × 3 m
= 723.6 × 106 m³
= 7.236 × 108 m³
Since 7.236 × 108 m³ is approximately equivalent to 7.28 × 108 m³, therefore, we can say that total rainfall in the valley was approximately equivalent to the addition of normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
☛ Check: Class 10 Maths NCERT Solutions Chapter 13
Video Solution:
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 Question 4
Summary:
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km², we have proven that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
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