Question

The outer circumference of a circular track is 220m.The track is 7 metre wide everywhere.Calculate the cost of levelling the track at the rate of 50 paise per square metre.

Answer 1

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$\underline{SOLUTION}$ ➡

Given,

The outer circumference of the circular track = 220 m

Let,

The radius of the circular track = r

A.T.Q,

$2\pi \: r \: = 220 \\ \\ = > 2 \times \frac{22}{7} \times r = 220 \\ \\ = > \frac{44}{7} \times r = = 220 \\ \\ = > r = 220 \times \frac{7}{44} \\ \\ = > r = 35$

•°• Radius of the circular track = 35 m

•°• Area of the whole circular track

$= \pi \: r {}^{2} \\ \\ = \frac{22}{7} \times (35) {}^{2} \: \: \: sq \: .m \\ \\ = (\frac{22}{7} \times 1225) \: \: sq \: .m \\ \\ = 3850 \: \: sq \: .m$

Again,

Width of the track = 7 m

•°• Inner radius of the track = ( 35 - 7 ) m

= 28 m

•°• Area of the inner circular track

$= \pi \: r {}^{2} \\ \\ = \frac{22}{7} \times (28) {}^{2} \: \: \: sq \: .m \\ \\ = (\frac{22}{7} \times 784) \: \: sq \: .m \\ \\ = 2464\: \: sq \: .m$

•°• Area of the track = Area of the whole circular track - Area of the inner circular track

= ( 3850 - 2464 ) sq.m

= 1386 sq.m

Now,

Cost of levelling the track in per sq.m = 50 paise

= Rs. 0.50

•°• Cost of levelling in 1386 sq.m = Rs. ( 0.50 × 1386 )

= Rs. 693.00

$\underline{ANSWER}$ ➡ $\pink{\bold{\boxed{RS. \: 693.00}}}$

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