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The area of the circular garden is equal to the area of rectangle with length of 140 m and width of 110 m. Outside the garden, a road of 7 m width laid around the circular garden. If the cost of laying road is Rs. 5 per m2 then, what would be the cost of laying road (in Rs.)?

The area of the circular garden is equal to the area of rectangle with length of 140 m and width of 110 m. Outside the garden, a road of 7 m width laid around the circular garden. If the cost of laying road is Rs. 5 per m2 then, what would be the cost of laying road (in Rs.)? Correct Answer 16,170

Given:

Area of circular garden = Area of rectangle

Length of rectangle = 140 m

Breadth of rectangle = 110 m

Road width = 7 m

Rate of laying road = Rs. 5 per m2

Formula Used:

Area of rectangle = (length × breadth)

Area of circular garden = πr2

Calculation:

Area of rectangle = (140 × 110) = 15400 sq. m

Area of circular garden = πr2

⇒ 22/7 × r2 = 15400

⇒ r2 = 4900

⇒ r = √(4900)

⇒ r = 70 m

∴ OA = 70 m, OB = 77 m

Area of road = π(OB2 – OA2)

⇒ 22/7 × (772 – 702)

⇒ 22/7 × (5929 – 4900)

⇒ 22/7 × 1029

⇒ 22 × 147

⇒ 3234 sq. m

∴ Total cost of laying road = Rs. (3234 × 5)

⇒ Rs. 16,170

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