Question

13. Find the area of a sector of a circle of radius 28 cm and central angle 45°

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Answer 1

Topic :

Mensuration

Given :

A sector of circle of radius 28 cm and central angle 45°.

To Find :

Area of given sector.

Formula to be Used :

Area of Sector of a circle = (∅/2π) × πr²

Area of Sector of a circle = (1/2)r²(∅)

where

• ∅ is central angle of sector in radians.

• r is radius of Circle.

Solution :

Calculating 45° in radians.

360° = 2π radians

1° = (2π/360) radians

45° = (2π/360) × 45 radians

45° = (π/4) radians

Applying formula of Area of Sector

∅ = π/4 radians

r = 28 cm

Area of Sector = (1/2)r²(∅)

Area of Sector = (1/2)(28)²(π/4) cm²

Area of Sector = 1/8 × 784 × 22/7 cm²

Area of Sector = 1/8 × 112 × 22 cm²

Area of Sector = 14 × 22 cm²

Area of Sector = 308 cm²

Answer :

So, area of given sector is 308 cm².

Answer 2

QuestioN :

Find the area of a sector of a circle of radius 28 cm and central angle 45°.

GiveN :

• radius = 28 cm

• central angle = 45°

To FiNd :

• The area of a sector of a circle.

ANswer :

The area of a sector of a circle is 308cm²

SolutioN :

Given that,

Radius = 28 cm

central angle = 45°

Formula to be used,

Area of sector = central angle /360 × pi × r × r

Now Solving,

area of sector = central angle /360 × pi × r × r

⇒ 45/360 × 22/7 × 28 × 28

∴Hence, The area of a sector of a circle is 308cm²