Question

Find the area of the sector whose length of the arc is 58 cm. and the radius is 10 cm.​

Answer 1

Answer:

• Area of sector is 29 cm²

Explanation:

Given

• Length of arc of sector, l = 58 cm
• Radius of sector, r = 10 cm

To find

• Area of sector =?

Solution

Let, angle subtended by sector at centre be θ

then, using relation

→ θ = l / r

[ where θ is angle subtended on centre (In Radian unit), l is length of arc and r is radius ]

→ θ = 58 / 10

→ θ = 5.8 Rad

converting angle in radian into degree

→ θ = 5.8 Rad

→ θ = 5.8 × 180 / π  degrees

Now,

Using formula to calculate area of sector

→ Ar (sector) = (θ/360) × π r²

[ Where θ is angle subtended on centre in degrees & r is radius of sector ]

→ Ar (sector) = [(5.8 × 180 / π)/360] × π × ( 10 )²

→ Ar (sector) = ( 5.8 / 2 ) × 100

→ Ar (sector) = 5.8 × 50

→ Ar (sector) = 29 cm²

Therefore,

• Area of sector is 29 cm².

Answer 2

Question:-

Find the area of the sector whose length of the arc is 58 cm. and the radius is 10 cm.

Solution:-

Here, length of the arc , = 58 cm and r = 10cm

➭ Length of arc , 1 = θ/360° × 2πr

➭ 58 = θ/360 × 2π × 10

∴ θ = 58 × 360° = 1044/π

2π × 10

➭ Now, the area of sector , A = θ/360° × πr²θ

∴ A = 1,044/π × π × 10 × 10 = 275

360

☞ Hence verified