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

Answer:

Step-by-step 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 ]

$\bold{\blue{ Perimeter \: of \: Sector = }}{\bold{\blue{\dfrac{\theta}{360°}}}}{\bold{\blue{× 2πr + r + r }}}$

Subsitute the required values in the above formula :-

Length of the arc of OAB

$\sf{=}{\sf{\dfrac{ 60°}{360°}}}{\sf{×2πr + 2r }}$

$\sf{=}{\sf{\dfrac{ 6}{36}}}{\sf{×2×21π + 2 × 21 }}$

$\sf{= }{\sf{\dfrac{1}{6}}}{\sf{ × }}{\sf{\dfrac{22}{7}}}{\sf{× 42 + 42 }}$

$\sf{= }{\sf{\dfrac{1}{3}}}{\sf{ × }}{\sf{\dfrac{11}{7}}}{\sf{ × 42 + 42 }}$

$\sf{= }{\sf{\dfrac{1}{3}}}{\sf{× 11×6 + 42 }}$

$\sf{ = 11 × 2 + 42 }$

$\sf{= 22 + 42 }$

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

Thus, The perimeter of the sector OAB is 64 cm

Now,

We have to find the area of sector OAB

We know that,

$\bold{\blue{ Area \: of \: sector = }}{\bold{\blue{\dfrac{\theta}{360°}}}}{\bold{\blue{× πr² }}}$

Subsitute the required values in the above formula :-

Area of sector OAB

$\sf{=}{\sf{\dfrac{60°}{360°}}}{\sf{× πr² }}$

$\sf{=}{\sf{\dfrac{6}{36}}}{\sf{× π × 21 × 21 }}$

$\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× π × 21 × 21 }}$

$\sf{=}{\sf{\dfrac{1 }{6}}}{\sf{× 441π}}$

$\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× 441 × }}{\sf{\dfrac{22}{7}}}$

$\sf{=}{\sf{\dfrac{1}{6}}}{\sf{ × 63 × 22}}$

$\sf{=}{\sf{\dfrac{1}{6}}}{\sf{× 1386 }}$

$\bold{\red{= 231 \: cm²}}$

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.