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1. The circumference of a circular ground is 88 metres. A strip of land, 3 metres wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs Rs. 7 per square metre ?

A. Rs. 1050

B. Rs. 1125

C. Rs. 1325

D. Rs. 1650

Solution:

Let the radius of the ground be R metres.
Then,

\begin{aligned} \Rightarrow 2 π R = 88 \\ \Rightarrow R = (\frac{88 \times 7}{2 \times 22}) \\ \Rightarrow R = 14 m \end{aligned}

Area of land strip :

\begin{aligned} = π [{(14)}^{2} - {(11)}^{2}] m^{2} \\ = (\frac{22}{7} \times 25 \times 3) m^{2} \\ = (\frac{1650}{7}) m^{2} \end{aligned}

∴ Cost of levelling :

\begin{aligned} = Rs . (\frac{1650}{7} \times 7) \\ = Rs . 1650 \end{aligned}

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