24 the circle and outside the square. 25. A path of 4 m width runs round a semi-circular grassy plot whose circumference is 163 3 m Find: (i) the area of the path (ii) the cost of gravelling the path at the rate of 1.50 per square metre (ii) the cost of turfing the plot at the rate of 45 paise per m². 25. Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third non it
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A path of 4 m width runs round a circular grassy plot whose circumference a 163
7
3
m Find
(i) the area of the path
(ii) the cost of gravelling the path at the rate of Rs.1.50 per square meter
(iii) the cost of turfing the plot at the rate of 45 paise per m
2
.
Hard
Solution
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Circumference of plot=163
7
3
m
=
7
1144
m
⇒2πr=
7
1144
⇒r=
7×44
1144×7
⇒r=26m
i) Area of path=π(R
2
−r
2
)
=
7
22
((26+4)
2
−(26)
2
)
=
7
22
×224
=704m
2
ii) Cost of graveling
= (704×1.50)
= Rs.1056
iii) Area of plot=πr
2
=
7
22
×26×26
=2124.57m
2
∴ Cost of turfing at the rate of 45 paise per m
2
m2
=Rs.(2124.57×0.45)
=Rs.956.06
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