Question

The radius of a circular cricket ground is

76 m

. A drainage

2 m

wide has to be constructed around the cricket ground for the purpose of draining the rain water. Find the cost of constructing the drainage at the rate of

₹ 180

per square metre.

Accepted Answer

The radius of the inner circle (cricket ground), $r = 76 m$

A drainage is constructed around the cricket ground.

Therefore, the radius of the outer circle, $R = 76 + 2 = 78 m$

We have, area of the circular path $= π (R^{2} - r^{2})$

$= \frac{22}{7} \times (78^{2} - 76^{2})$

$= \frac{22}{7} \times (6084 - 5776)$

$= \frac{22}{7} \times 308$

$= 22 \times 44$

$= 968 m^{2}$

Given, the cost of constructing the drainage per square metre is $= ₹ 180$

Therefore, the cost of constructing the total drainage $=$ Area of the circular path $\times$ Cost of constructing the drainage per square metre

$= 968 \times ₹ 180 = ₹ 1, 74, 240$

Hence, the cost of constructing the total drainage is $₹ 1, 74, 240$ .

Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 17: Example 2.17

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 17: Example 2.17

Questions from Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 17: Example 2.17 with Hints & Solutions

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