Question

If the perimeter of a certain sector is 10 units and radius of the circle is 3 units, find the area of sector?

IIT { PRACTICE SET }

Answer 1

Heya!!
Here's your answer!!
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Radius of circle = 3 unit

Perimeter of an arc = 10 units

Length of that arc = Perimeter of arc - 2 × Radius of that circle

= 10 units - 2× 3 units

= 10 units - 6 units = 4units

Perimeter of circle = 2πr

= 2(22/7)3 unit

= (132/7) unit

Area of circle = πr²

= (22/7)×(3 units)²

= (22/7)× 9 unit²

= (198/7) unit²

To find the area of a sector we have a formula,

Area of a sector = (center angle/360°) × area of circle

Now,

Let the center angle is a

= (360°/a) = perimeter of circle ÷ length of arc

=> (360°/a) = perimeter of circle ÷ length of arc

=> (360°/a) = (132/7) unit ÷ 4unit

=> (360°/a) = (132/7 × 4)

=> (360°/a) = (33/7)

=> a = (360°×7) ÷ 33

=> a = (120°×7) ÷ 11

∴ a = 840/11

Now,

Area of sector = (a/360°) × Area of circle

= {( 840°/11) ÷ 360°} × (198/7) units²

= {840°/11×360°) × (198/7) units²

= (7/11×3) × (198/7) units²

= (7/33) × (198/7) units²

= (198/33) unit²

= 6 units²

The required answer is 6 unit²
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@vaibhavhoaz
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Answer 2

Hello Friend..✌️✌️

The answer of u r question is..⬇️⬇️

Is in the pic..❤️❤️

Thank you..⭐️⭐️