the radius of a circular field is 35m.on itsoutside ,there is a path 5m wide . find the cost of levelling the path at ₹5.50 per sq m.
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radius =35 m
area= 3850sq.m
big radius=35+5. =40m
new area=5028.57sq.m
area of path=5028.57-3850
=1178.57sq.m
cost of levelling=1178.57*5.50=64821.35. rupees
area= 3850sq.m
big radius=35+5. =40m
new area=5028.57sq.m
area of path=5028.57-3850
=1178.57sq.m
cost of levelling=1178.57*5.50=64821.35. rupees
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Solution :
The radius of the circular field,
r = 35 m
Now, the area of the circular field
= πr² m²
= π * 35² m²
= 1225π m²
Given that, the width of the path is 5 m
Now, the radius of the circular field along with the path around it
= (radius of the circular field) + (width of the path)
= 35 + 5 m
= 40 m
So, the area of the of the circular field along with the path around it
= π (40)² m²
= 1600π m²
Thus, the area of the path
= (the area of the circular field along with the path around it) - (the area of the circular field) m²
= (1600π - 1225π) m²
= 375π m²
Thus, the cost of levelling the path at Rs 5.50 per m²
= Rs (5.50 * 375π)
= Rs (5.50 * 375 * 22 / 7)
= Rs 6482.14
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