Question

A road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of road.

Answer 1

Given:

• The circumference of the inner circular park = 352 m
• The width of the road = 7 m

Step 1: Find the radius of the park

We know,

Circumference = 2πr

So,

352 = 2 × π × r

Take π = `22/7`

`352 = 2 xx 22/7 xx r`

Multiply both sides by 7:

352 × 7 = 44r

2464 = 44r

`r = 2464/44 = 56 m`

So, the radius of the park is 56 m.

Step 2: Outer radius of the road

The road surrounds the park, so:

Outer radius = 56 + 7 = 63m

Step 3: Find the area of the road

Area of road = π(R² − r²)

where R = 63 m, r = 56

Area of road= `22/7 (63^2 - 56^2)`

Compute step-by-step:

632 = 3969, 562 = 3136

3969 − 3136 = 833

Area= `22/7 xx 833 = 22 xx 119 = 2618 m^2`

The area of the road is 2618 m².