Question

in a circle of diameter 20 cm, if an arc subtends an angle of 90° at the centre where π=3.14, then the area of the minor sector is


A) 78.5 cm
B) 157 cm
C) 314 cm
D) None of the above​

Answer 1

Answer:

Area of the minor sector is $78.5cm^2$.

Step-by-step explanation:

Given diameter of a circle, $d=20cm$.

Angle subtended at the centre is $\theta=90$°.

Area of a sector is $A=\frac{\theta}{360}\times \pi r^2$

where $\theta$ is the angle subtended at the centre

$r$ is radius of the circle.

We know that, diameter is twice the radius.

$d=2r$

$r=\frac{20}{2}$

$r=10cm$

Now substituting the values in the formula for area, we get

Area, $A=\frac{90}{360}\times \pi (10)^2$

$A=\frac{1}{4}\times 100\pi$

$A=25\pi$

Taking the value of pi as 3.14, we get

$A=78.5cm^2$

Therefore, the area of the minor sector is $78.5cm^2$.

Answer 2

Given,

In a circle of diameter $20cm$, if an arc subtends an angle of $90^{0}$ at the center

Where $\pi =3.14$

We have to find the area of minor sector

Here

Diameter $d= 20cm$

We know that

Diameter $= 2\times$ radius

$r=\frac{d}{2}$

radius $\frac{20}{2}=10cm$

An arc subtends an angle θ$= 90^{0}$

Formula for minor sector

Area of minor sector $A=$θ$/360$$\times \pi r^{2}$

We have to substitute given values in the above formula,

$A= \frac{90}{360}\times \pi \times 10$

$= \frac{1}{4}\times \pi \times 10$

$=25\pi$

Here $\pi =3.14$

$= 25\times 3.14$

$=78.5$

Therefore, the area of the minor sector is $78.5cm$.