The outer circumference of a circular race-track is 528 m. The track is every­where 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre (Use $\pi= \frac{22}{7}$).

Given:

The outer circumference of a circular race-track is 528 m. The track is every­where 14 m wide.

To do:

We have to calculate the cost of levelling the track at the rate of 50 paise per square metre.

Solution:

Let $R$ and $r$ be the radii of the outer and inner of the track.

Outer circumference of the race track $= 528\ m$

Width of the track $=14 \mathrm{~m}$

Outer radius $\mathrm{R}=\frac{\text { Circumference }}{2 \pi}$

$=\frac{528 \times 7}{2 \times 22} \mathrm{~m}$

$=12 \times 7$

$=84 \mathrm{~m}$

Therefore,

Inner radius $r=84-14=70 \mathrm{~m}$

Area of the track $=\pi R^{2}-\pi r^{2}$

$=\pi(\mathrm{R}^{2}-r^{2})$

$=\frac{22}{7}(84^{2}-70^{2}) \mathrm{m}^{2}$

$=\frac{22}{7}(84^2-70^2) \mathrm{m}^{2}$

$=\frac{22}{7} \times (7056-4900)$

$=6776 \mathrm{~m}^{2}$

Rate of levelling the track $=0.50$ per $\mathrm{m}^{2}$ Total cost of levelling the track $=Rs.\ 6776 \times 0.5$

$=Rs.\ 3388$

The total cost of levelling the track is Rs. 3388.

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Updated on: 10-Oct-2022

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