Question

What is the area of the sector whose diameter is 40 mm and angle is 120 degrees

Answer 1

Given :-

• Diameter = 40 mm
• Central angle = 120°

To Find :-

• Area of sector = ?

Answer :-

Area of sector = 419.04 mm²

Explaination:-

First of all we will calculate radius :

➝ Radius = Diameter ÷ 2

➝ Radius = 40 ÷ 2

➝ Radius = 20 mm

Now, let's find the area of sector :

As we know that Area of sector is calculated by :

• Area of sector = (ϴ/360°) πr²

Where r is radius, ϴ is central angle in degrees and π = 22/7.

Now, subsitute the given values in above formula :-

⇢ Area of sector = 120°/360° × 22/7 × 20 × 20

⇢ Area of sector = 12/36 × 22/7 × 400

⇢ Area of sector = 6/18 × 22/7 × 400

⇢ Area of sector = 3/9 × 22/7 × 400

⇢ Area of sector = 1/3 × 22/7 × 400

⇢ Area of sector = 419.04 mm²

Therefore,area of sector is 419.04 mm².

Answer 2

Question :-

What is the area of the sector whose diameter is 40 mm and angle is 120 degrees.

Answer :-

$\red{\bigstar}$ Area of sector [A]

$\huge\leadsto{\sf\purple{507.04 \: mm}}$

Given :-

Diameter of the sector is 40 mm

Angle given as 120°.

Have to Find :-

What is the area of sector ?

Solution :-

Here we go !

Let's find out radius First :-

As we alll know radius is the half of the Diameter .

So , it would be 44/ 2

That is 22 mm

Then , simply applying the formula

Area of sector = (ϴ/360°) πr²

So , put the values and just calculate it :-

Area of sector = 120°/360° × 22/7 × 22 × 22

= 12/36 × 22/7 × 484

= 6/18 × 22/7 × 484

= 3/9 × 22/7 × 484

= 1/3 × 22/7 × 484

= 507.04 mm²

$\therefore\underline{\boxed{\textsf{A= {\textbf{507.04mm}}}}} \qquad\qquad \bigg\lgroup\bold{Area \ of \ sector } \bigg\rgroup$

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