Question

Find the area and perimeter of a sector of a circle with radius 6 cm if the angle of the sector is 60

Answer 1

$\Huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

...Given...

• Radius is 6 cm
• And Angle of the sector is 60°

$\rule{200}{2}$

Formula for Perimeter of Sector is :

$\LARGE \implies {\boxed{\boxed{\sf{2r \: + \: \frac{2 \pi r \theta}{360^{\circ}}}}}}$

Where r is radius = 6 cm

θ = 60°

⇒ Perimeter = 2(6) + [2π(6) * 60°/360°]

⇒ Perimeter = 12 + 2π

⇒Perimeter = 12 + 2(22/7)

⇒Perimeter = 12 + 6.28

⇒Perimeter = 18.28

$\Large{\boxed{\red{\sf{Perimeter \: = \: 18.28 \: cm}}}}$

$\rule{200}{2}$

And formula for Area of sector is :

$\LARGE \implies {\boxed{\boxed{\sf{\frac{\pi r^2 \theta}{360^{\circ}}}}}}$

Put Values

⇒ Area = π * (6)² * 60/360

⇒Area = 6π

⇒Area = 6 * 22/7

⇒Area = 18.85 cm²

$\Large{\boxed{\red{\sf{Area \: = \: 18.85 \: cm^2}}}}$

Answer 2

CONCEPT :

➦ We need to multiply the square of the radius with π = 22 / 7 to get the area of the circle. This area of the circle is multiplied with the quotient obtained on dividing 60° by 360 ° to get the area of the sector of a circle.

REQUIRED ANSWER :

➜ We are given a circle with radius 6 cm.

Also, we are given that the angle of a sector of this circle is 60∘.

➜ We are asked to compute the area of this sector of the circle.

➜ Let’s have a look at the figure of this circle.

➜ The shaded portion is the sector for which we are to find the area.

➜ If the angle θ measured in degrees, then the area of the sector of the circle is given by the formula

★ Area of sector = θ / 360° × πr ^2

➜ Where r is the length of the radius of the circle and θ is the angle of the sector.

➜ We have θ = 60∘ and r = 6 cm. Take π = 22 / 7

Therefore, on substituting, we get

★ Area of sector

➜ 60° / 360° × 22 / 7 × 6^2 = 22 / 7 × 6 ≈ 18 . 86 cm^ 2

Hence the required area is 18.86cm^2

KNOW MORE :

★ use the formula for area of sector wrongly. Instead of πr ^2 they tend to use 2 π r in the formula. This will give you the length of the arc and not the area of the sector because 2 π r is the length of the circumference of the circle.