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Question
A 4.2m wide road surrounds a circular plot whose circumference is 176m. Find the cost of paving the road at Rs.75per m2.
Solution
We know,
The area of the ring between two concentric circles equals the area of the larger circle minus the area of smaller circle.
Let the radius of the outer and inner ring be R and r respectively.
Here the circular garden is the inner circle and the 7m wide road is the ring
The Circumference of a Circle with radius r = 2πr
Here,
2πr = 176
⇒ r = `(176)/(2π)`
= `(176 xx 7)/(2 xx 22)`
= 28
⇒ r = 28m
⇒ R = 28 + 4.2
= 32.2m
inner Circle has radius r
= 28m and outer Circle has radius R
= 32.2m
π(32.22 - 282)
= `(22)/(7) xx (1036.84 - 784)`
= `(22)/(7) xx 252.84`
= 794.64m2
The cost of paving the road at the rate of Rs.150per m2
= 794.64 x 75
= Rs.59,598.
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