A rectangular lawn whose length is twice of its breadth is extended by having four semi-circular portions on its sides. What is the total cost (in ₹) of levelling the entire lawn at the rate of ₹100 per square metre, if the smaller side of the rectangular lawn is 12m? (Take π = 3.14)
Answer & explanation
Correct answer: option 1
We know that,
Area of rectangle = Length × Breadth
Area of semi-circle = \(\frac{1}{2}\) × πr2
We have,
Length = 2 × Breadth
Breadth = 12m
Length = 2 × Breadth
Length = 2 × 12 = 24 m
Area of rectangle = Length × Breadth = 12 × 24 = 288 m2
Area of semi-circle on larger side = \(\frac{1}{2}\) × π × 122 = 72π m2
Area of semi-circle on smaller side = \(\frac{1}{2}\) × π × 62 = 18π m2
Total area of lawn = Area of rectangle + 2 × Area of semi-circle on larger side + 2 × Area of semi-circle on smaller side
= 288 + (2 × 72π ) + (2 × 18π)
= 288 + 2π(72 + 18)
= 288 + 2 × 3.14 × 90
= 288 + 565.2 = 853.2 m2
Total cost of levelling = Total area of lawn × 100
= 853.2 × 100 = 85320