Question

The circumference of a circle is 88 cm. Find the area of the sector whose central angle is 72°.

Answer 1

Given:

Circumference C = 88 cm

Central angle θ = 72°

Step-wise calculation:

1. Circumference formula:

C = 2πr 

⇒ `r = C/(2π)` 

= `(88)/(2π)` 

= `(44)/π` cm

2. Area of a sector:

`A = (θ/360) xx πr^2`

3. Compute r²:

`r^2 = (44/π)^2` 

= `(1936)/π^2`

4. Substitute into sector area:

`A = (72/360) xx π xx (1936/π^2)` 

= `(1/5) xx π xx (1936/π^2)` 

= `(1936)/(5π) cm^2`

5. Decimal approximation:

`A ≈ (1936)/(5·3.14159265)` ≈ 123.2 cm²