A 36º sector of a circle has area 3.85 cm2. What is the length of the

1.	A 36º sector of a circle has area 3.85 cm2. What is the length of the arc of the sector?(a) 1.1 cm (b) 3.5 cm (c) 5 cm (d) 2.2 cm
Answer» Answer : (d) 2.2 cm Area of a sector = \(\frac{\theta}{360^0}\) × \(\pi r^2\) ⇒ \(\frac{36}{360}\) × \(\frac{22}{7}\) × r² = 3.85 ⇒ r² = \(\frac{3.85 \times 10\times 7}{22}\) = 12.25 ⇒ r = 3.5 cm. ∴ Length of arc = \(\frac{\theta}{360^0}\) × \(\pi r^2\) = \(\frac{36}{360}\) × 2 × \(\frac{22}{7}\)× 3.5 = 2.2 cm

A 36º sector of a circle has area 3.85 cm2. What is the length of the arc of the sector?(a) 1.1 cm (b) 3.5 cm (c) 5 cm (d) 2.2 cm

Answer»

Answer : (d) 2.2 cm

Area of a sector = \(\frac{\theta}{360^0}\) × \(\pi r^2\)

⇒ \(\frac{36}{360}\) × \(\frac{22}{7}\) × r² = 3.85

⇒ r² = \(\frac{3.85 \times 10\times 7}{22}\) = 12.25

⇒ r = 3.5 cm.

∴ Length of arc = \(\frac{\theta}{360^0}\) × \(\pi r^2\)

= \(\frac{36}{360}\) × 2 × \(\frac{22}{7}\)× 3.5

= 2.2 cm