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Question

# The inner circumference of a circular track is 440 m, and the track is 14 m wide. Calculate the cost of levelling the track at 25 paise/m2. Also, find the cost of fencing the outer boundary of the track at Rs 5 per metre.

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Solution

## Let the radius of the inner circle be r m.Now,Inner circumference = 440 m$⇒2\mathrm{\pi r}=440$$⇒2×\frac{22}{7}×r=440\phantom{\rule{0ex}{0ex}}⇒r=\frac{440×7}{44}\phantom{\rule{0ex}{0ex}}⇒r=70$We know that the track is 14 m wide.∴ Outer radius (R) = (70 + 14) = 84 m $\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{track}=\mathrm{\pi }\left({\mathrm{R}}^{2}-{r}^{2}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{\pi }\left({84}^{2}-{70}^{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{22}{7}×\left(7056-4900\right)\phantom{\rule{0ex}{0ex}}=6776 {\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}$Cost of levelling at 25 paise per square metre $=6676×25=169400\mathrm{paise}$Or,$\mathrm{Rs}\frac{169400}{100}=\mathrm{Rs}1694$​∴ Outer circumference = $2\mathrm{\pi R}$$=2×\frac{22}{7}×84\phantom{\rule{0ex}{0ex}}=528\mathrm{m}$Rate of fencing = 5 per metre∴ Total cost of fencing $=528×5=\mathrm{Rs}2640$

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