Given:
central angle of a sector = 15°
The area of a sector = 231cm²
Find:
circumference(in cm) of the circle
Solution :
we know that,
Area of sector with central angle as θ , and radius of circle as r is = (θ/360°) * π * (r)² .
given that,
- θ = 15°
- Area of sector = 231 cm².
- radius of circle = Let r.
Putting values we get,
→ (θ/360°) * π * (r)² = 231
→ (15°/360°) * (22/7) * r² = 231
→ (1/24) * (22/7) * r² = 231
→ 22 * r² = 231 * 7 * 24
dividing both sides by 2,
→ 11 * r² = 231 * 7 * 12
dividing both sides by 11,
→ r² = 21 * 7 * 12
→ r² = (7 * 7) * (3 * 3) * 4
→ r² = (7² * 3² * 2²)
→ r² = (7 * 3 * 2)²
→ r² = (42)²
square root both sides,
→ r = 42 cm.
Therefore ,
→ circumference of the circle = 2 * π * radius .
→ circumference of the circle = 2 * (22/7) * 42
→ circumference of the circle = 44 * 6
→ circumference of the circle = 264 cm .
Hence, circumference of the circle is 264 cm.
I hope it will help you.
Regards.