Question

The perimeter of the sector of a circle with central angle 90° is 25 cm find the area of the minor Segment

Answer 1

Given:

A sector has a central angle of 90°.

Perimeter of sector is 25 cm

To find:

Area of minor segment = ?

Solution:

First of all, please refer to the attached image for the given dimension.

It is given that central angle is 90°.

We know that central angle for the whole circle is 360°.

90° is the one fourth of the whole circle.

$\therefore$ perimeter of sector = $\frac{1}{4} \times \text{Perimeter of circle}$

$\Rightarrow 25 = \dfrac{1}{4}\times 2\pi r\\\Rightarrow r = \dfrac{50}{\pi}$

Where r is the radius of circle.

Now, area of minor segment = $\frac{1}{4} \times \text{Area of circle}$

$\Rightarrow \dfrac{1}{4}\times \pi r^2\\\Rightarrow \dfrac{1}{4}\times \pi (\frac{50}{\pi})^2\\\Rightarrow \dfrac{625}{\pi}\\\Rightarrow \dfrac{625}{3.14}\\\Rightarrow 199.04\ cm^2$

Answer 2

Answer:

The above given answer is wrong .I don't know how it became expert-verified but its wrong.The user forgot to include:

Perimeter of a sector of a circle = 1/4 of perimeter of circle + 2(Radii)

So the whole calculation is wrong...

Correct answer will be 14cm square

Step-by-step explanation: