Question

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 Rs.) of levelling the entire lawn at the rate of Rs. 100 per square metre, if the smaller side of the rectangular lawn is 12 m? (Take π = 3.14)

• A. 86,540
• B. 78,650
• C. 85,320
• D. 97,625

Answer 1

Answer:

C. 85,320

Solution:

Given:

Length = 2 × Breadth

Breadth = 12m

Cost of levelling = Rs. 100/m²

Formula used:

Area of rectangle = Length × Breadth 

Area of semi-circle = 1/2 × πr²

Calculation:

Length = 2 × Breadth

⇒ Length = 2 × 12

⇒ Length = 24 m

Area of rectangle = Length × Breadth 

⇒ Area of rectangle = 12 × 24

⇒ Area of rectangle = 288 m²

Area of semi-circle on larger side = 1/2 × π × 12²

⇒ Area of semi-circle on larger side = 72π m²

Area of semi-circle on smaller side = 1/2 × π × 62

⇒ Area of semi-circle on smaller side = 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

⇒ Total area of lawn = 288 + (2 × 72π ) + (2 × 18π)

⇒ Total area of lawn = 288 + 2π(72 + 18)

⇒ Total area of lawn = 288 + 2 × 3.14 × 90

⇒ Total area of lawn = 288 + 565.2

⇒ Total area of lawn = 853.2 m²

Total cost of levelling = Total area of lawn × 100

⇒ Total cost of levelling = 853.2 × 100

⇒ Total cost of levelling = Rs. 85320

∴ The total cost of levelling the entire lawn is Rs. 85320.

Alternate Method 

Length = 2 × Breadth

⇒ Length = 2 × 12

⇒ Length = 24 m

Area of rectangle = Length × Breadth 

⇒ 12 × 24 = 288 m2

Area of semi-circle on larger side = 1/2 × π × 122

⇒ 72π m2

Area of semi-circle on smaller side = 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