Question

In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π?

Answer 1

Answer:

The Area of the sector of a circle is 30π cm² .

Step-by-step explanation:

Given :  

Angle subtended by an Arc,  θ = 108°

Radius of a circle ,r = 10 cm

Area of the sector of a circle, A = (θ/360) × πr²

A = (108°/360°) π ×10²

A = (3/10) × 100 π

A = (3 × 10 π)

A = 30π cm²

Area of the sector of a circle = 30 π cm²

Hence, the Area of the sector of a circle is 30π cm² .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

An arc subtends an angle of

θ = 108° at the centre of a circle of radius r = 10 cm.

To find the area of the sector.

The area of the sector of a circle of radius r subtending an angle of θ is,

$A = \:\frac{\theta}{360} \times\pi \: r {}^{2}$

By substituting the given values in the

above equation, we have

$area \: of \: sector \: = \frac{108}{360} \times \pi \times {10}^{2} \\ \\ further \: solving \: the \: equation \: \: we \: get \\ \\ area \: of \: sector \: = \frac{3}{10} \times \pi \times 100 \\ \\ area \: of \: sector \: = 3 \times \pi \times 10 \\ \\ area \: of \: sector \: = 30\pi$

Therefore, the area of the sector formed by an arc subtending an angle of 108° at the centre of a circle of 30π cm^2