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 ₹ 130/- per sq.m.
[3 marks]

Answer 1

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
= $\pi$($R^2$ - $r^2$) sq.units [1 mark]
= $\frac{22}{7}$ $\times$ ( ${78}^2$- ${76}^2$)
= $\frac{22}{7}$ $\times$ ( 6084 - 5776)
= $\frac{22}{7}$ $\times$ 308
= 22 $\times$ 44 = 968 $m^2$ [1 mark]

Given, the cost of constructing the drainage per sq.m is ₹130.
Therefore, the cost of constructing the drainage = 968 x 130 = ₹ 1,25,840 [1 mark].