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Maths-

General

Easy

Question

A road 3.5 m wide surrounds a circular park whose circumference is 44 m. Find the cost of paving the road at Rs. 20 per m²

hint Hint:

Area of the road is the difference of the areas of two circles

The correct answer is: Rs. 3850

It is given that Circumference of the circular park = 44
2 $straight pi$ r = 44
2 × $22 over 7$ r = 44
r = 7 cm
Radius of outer circle
r₁ = Radius of circular park + Width of the par
= 7 + 3.5 = 10.5 cm
Area of the road = Area of outer circle – Area of inner circle
= $straight pi$ (r₁)² - $straight pi$ r²
= $22 over 7$ × (10.5)² - $22 over 7$ × (7)²
= $22 over 7$ × (10.5 – 7)(10.5 + 7)
= $22 over 7$ × 3.5 × 17.5
= 192.5 cm²
Cost of paving 1 cm² road = Rs. 20
Cost of paving 192.5 cm² road = Rs. 20 × 192.5
= Rs. 3850

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