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Maths-

General

Easy

Question

The diameter of a circular park is 94.4 m. A 2.8 m wide road is constructed outside this circular park, i.e., around it. Find the cost of paving this road at the rate of Rs. 50 square meter

hint Hint:

Try to find area of the road

The correct answer is: Rs. 42768

Since the road of width 2.8 m is on outside , it means
Diameter of inner circle = 94.4 m
$rightwards double arrow$ Radius = $fraction numerator text diameter end text over denominator 2 end fraction$ = $fraction numerator 94.4 over denominator 2 end fraction$ = 47.2 m
We know that area of a circle = p r²
Radius of outer circle = Radius of inner circle + Width of road
= 47.2 + 2.8 = 50 m
Area of the road = Area of outer circle – Area of inner circle
= $22 over 7$ × (50)² - $22 over 7$ × (47.2)²
= $22 over 7$ × ( 50 – 47.2)(50 + 47.2)
( $therefore$ a² – b²) = (a – b)(a + b)
= $22 over 7$ 2.8 × 97.2
= 855.36 m²
Now, Cost of constructing 1 m² road = Rs. 5
Cost of constructing 855.36 m² road = Rs. 50 855.36
= Rs. 42768

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