Question

length of the arc =48m radius=10m find the area of the sector​

Answer 1

Answer:

here ,

l = 48cm

r = 10cm

so, are of the sector = ½ × l × r

= ½ × 10 × 48

= 10 × 24

= 240 cm²

Answer 2

The area of the sector is 240 m².

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Let's understand a few concepts:

To find the area of the given sector we will use the following two formulas:

• If θ is measured in radians then $\boxed{\bold{Arc\: length = \theta\times r}}$

• If θ is measured in radians then $\boxed{\bold{Area\:of\: sector = \frac{1}{2} \times r^2\times \theta}}$

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Let's solve the given problem:

Step 1:

The length of the arc of the given sector = 48 m

The radius (r) = 10 m

Step 2:

By using the above formula of the arc length and substituting the given values of r and arc length, we can form an equation as,

$48 = \theta \times 10$

$\implies \theta = \frac{48}{10}$

$\implies \theta = 4.8$ . . . (1)

Step 3:

Now, by substituting the value of θ from equation (1) and radius r = 10 m in the above formula for the area of the sector, we get

The area of the given sector is,

= $\frac{1}{2} \times r^2\times \theta}}$

= $\frac{1}{2} \times 10^2\times 4.8$

= $\frac{1}{2} \times 100\times 4.8$

= $50\times 4.8$

= $\bold{240 \:m^2}$

Thus, the area of the sector is 240 m².

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