Question

The area of a sector of a circle is 616 cm2 with a central angle of 10°. The radius of the circle is ______. (use π =$\frac{22}{7}$ )

• A. 84 cm
• B. 21 cm
• C. 48 cm
• D. 28 cm

Answer 1

Answer:

A. 84 cm

Solution:

Given:

Area of a sector of a circle = 616 cm² 

Angled formed at the centre by arc = 10° 

Concepts used:

Area of a sector of circle = πr² × (θ/360°) 

Where,

θ → Angle formed at the centre

r → Radius of circle

Calculation:

Let the radius of the circle be r cm.

Area of sector of circle = πr2 × (θ/360°) 

⇒ 616 cm² = πr² ×  (10°/360°) 

⇒ 616 cm² = (1/36) × (22/7) × r² 

⇒ 616 cm² = (22/28) × r² 

⇒ r² = (616 × 36 × 7)/22

⇒ r = √ (28 × 36 × 7)

⇒ r = 84 cm.

∴ The radius of the circle is 84 cm.