Question

A path of 4 m width runs round a circular grassy plot whose circumference is `163 3/7` m Find:

1. the area of the path
2. the cost of gravelling the path at the rate of ₹ 1.50 per square metre
3. the cost of turfing the plot at the rate of 45 paise per m².

Answer 1

Given:

Width of path = 4 m

Circumference of grassy plot = `163 3/7` m = `1144/7` m

Use `π = 22/7`.

Step-wise calculation:

1. Find radius of the grassy plot.

Circumference = 2πr

⇒ `1144/7 = 2 xx (22/7) xx r` 

⇒ `1144/7 = 44/7 xx r`

⇒ `r = 1144/44` = 26 m

2. Outer radius (including path) = 26 + 4 = 30 m

3. Area of the path = `π(R^2 - r^2)`

= `(22/7) xx (30^2 - 26^2)`

= `(22/7) xx (900 - 676)`

= `(22/7) xx 224` 

= 22 × 32

= 704 m²

4. Cost of gravelling the path at ₹ 1.50/m²

= 704 × 1.50

= ₹ 1056.00

5. Area of the grassy plot = πr²

= `(22/7) xx 26^2`

= `(22/7) xx 676`

= `14872/7` ≈ 2124.5714 m²

Cost of turfing at 45 paise/m² = ₹ 0.45/m²

= 2124.5714 × 0.45 ≈ ₹ 956.0571 ≈ ₹ 956.06

i. Area of the path = 704 m².

ii. Cost of gravelling the path = ₹ 1056.00.

iii. Cost of turfing the plot = ₹ 956.06 (rounded to paise).