Question

The angle in the sector is 60⁰ and the radius is 7 cm. Then the area of the sector is ____ (approximately)

a)11

b)15

c)26

d)21​

Answer 1

Answer:

• The area of the sector is 26cm², option (c) 26 is correct option.

Explanation:

Given, we have the angle of sector and the radius of sector and we exigency to devise the area of sector.

We know that, if we are given with the angle of sector and radius of sector, then we have the required formula, that is,

→ Area of sector = θ/360° × πr²

Here,

• θ denotes the angle of sector.
• The value of π is 22/7.
• r denotes the radius of sector.

Values,

• θ = 60°.
• π = 22/7.
• r = 7cm.

By using the required formula, and substituting all the given values in the formula, we get:

→ Area of sector = 60/360 × 22/7 × (7)²

→ Area of sector = 6/36 × 22/7 × 7 × 7

→ Area of sector = 1/6 × 22/7 × 7 × 7

→ Area of sector = 1/6 × 22 × 7

→ Area of sector = 1/3 × 11 × 7

→ Area of sector = 1/3 × 77

→ Area of sector = 77/3

→ Area of sector = 25.66

→ Area of sector ≈ 26. (approx.)

Hence, the area of sector is 26cm², option (c) is correct.

Answer 2

Answer:

Given :-

• The angle in the sector is 60° and the radius is 7 cm.

To Find :-

• What is the area of the sector.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Area\: of\: Sector =\: {\pi}{r}^{2} \times \bigg(\dfrac{\theta}{360^{\circ}}\bigg)}}}$

• $\theta$ = Angle of sector
• r = Radius of sector

Solution :-

Given :

• Angle of sector = 60°
• Radius of sector = 7 cm

According to the question by using the formula we get,

$\implies \sf Area\: of\: sector =\: \dfrac{22}{7} \times {(7)}^{2} \times \bigg(\dfrac{60}{360}\bigg)$

$\implies \sf Area\: of\: sector =\: \dfrac{22}{7} \times 49 \times \bigg(\dfrac{60}{360}\bigg)$

$\implies \sf Area\: of\: sector =\: \dfrac{1078}{7} \times \dfrac{60}{360}$

$\implies \sf Area\: of\: sector =\: \dfrac{1078 \times 60}{7 \times 360}$

$\implies \sf Area\: of\: sector =\: \dfrac{6468\cancel{0}}{252\cancel{0}}$

$\implies \sf Area\: of\: sector =\: \dfrac{\cancel{6468}}{\cancel{252}}$

$\implies \sf Area\: of\: sector =\: 25.67$

$\implies \sf Area\: of\: sector =\: 26(approx)$

$\implies \sf\bold{\red{Area\: of\: sector =\: 26\: {cm}^{2}}}$

$\therefore$ The area of sector is 26 cm².

Hence, the correct options is option no (c) 26 .