Question

find the area and perimeter of sector OAB given that angle AOB is 60 degrees and the radius of a circle is 21cm​

Answer 1

Explanation:

Perimeter of a sector

The circumference of a circle is 2 pi r.

pi = 3.14

r = 21 cm

The angle of this particular sector is 60 degrees.

So the formula for this sector is P = 2*r + 60/360 * 2* pi * r

Now all you need do is plug the numbers in.

P = 2 * 21 + 1/6 * 2 * 3.14 * 21

P = 42 + 21.98

P = 63.98

Area of the sector

Area of a circle = pi * r^2

Area of a sector = theta / 360 * pi * r^2

theta = 60 degrees

area of this sector = (60/360) * 3.14 * 21^2

Area of this sector = (1/6) * 3.14 * 441

Area of this sector = 230.79

Answer 2

`\bold{\huge{\pink{\underline{ Solution }}}}`

Given :-

• We have given that, Angle AOB is 60°
• The radius of the circle is 21cm

To Find :-

• We have to find the area and perimeter of the sector OAB

Let's Begin :-

We have ,

• Two radii of the circle OA and OB = 21 cm each
• 
  `\bold{\angle{ AOB = 60° }}`
• AB is the segment of the circle

We know that,

[ Perimeter of sector = Arc length + radius + radius ]

`\bold{\blue{ Perimeter \: of \: Sector = }}{\bold{\blue{(\theta)/(360°)}}}{\bold{\blue{× 2πr + r + r }}}`

Subsitute the required values in the above formula :-

Length of the arc of OAB

`\sf{=}{\sf{( 60°)/(360°)}}{\sf{×2πr + 2r }}`

`\sf{=}{\sf{( 6)/(36)}}{\sf{×2×21π + 2 × 21 }}`

`\sf{= }{\sf{(1)/(6)}}{\sf{ × }}{\sf{(22)/(7)}}{\sf{× 42 + 42 }}`

`\sf{= }{\sf{(1)/(3)}}{\sf{ × }}{\sf{(11)/(7)}}{\sf{ × 42 + 42 }}`

`\sf{= }{\sf{(1)/(3)}}{\sf{× 11×6 + 42 }}`

`\sf{ = 11 × 2 + 42 }`

`\sf{= 22 + 42 }`

`\bold{\red{= 64 \: cm}}`

Thus, The perimeter of the sector OAB is 64 cm

Now,

We have to find the area of sector OAB

We know that,

`\bold{\blue{ Area \: of \: sector = }}{\bold{\blue{(\theta)/(360°)}}}{\bold{\blue{× πr² }}}`

Subsitute the required values in the above formula :-

Area of sector OAB

`\sf{=}{\sf{(60°)/(360°)}}{\sf{× πr² }}`

`\sf{=}{\sf{(6)/(36)}}{\sf{× π × 21 × 21 }}`

`\sf{=}{\sf{(1)/(6)}}{\sf{× π × 21 × 21 }}`

`\sf{=}{\sf{(1 )/(6)}}{\sf{× 441π}}`

`\sf{=}{\sf{(1)/(6)}}{\sf{× 441 × }}{\sf{(22)/(7)}}`

`\sf{=}{\sf{(1)/(6)}}{\sf{ × 63 × 22}}`

`\sf{=}{\sf{(1)/(6)}}{\sf{× 1386 }}`

`\bold{\red{= 231 \: cm²}}`

Hence, The area and perimeter of the sector OAB is 64 cm and 231cm²

What is sector?

• Sector is nothing but the portion covered by the two radii of the circle
• For example, In the given circle
• OAB is sector as it is enclosed by two radii OA and OB.