Question

Find the area of the 1 /4 part of a circle with the radius of 3. 5 cm

Answer 1

ANSWER:

Let us divide the circle into 4 equal parts because they have told that 1/4 th part so there are 4 equal parts because,fractions represent equal parts of a whole or a collection.

Let us take a circle with centre 'O'

Now, the 1/4th part of circle is a sector with angle 90° & radius 3.5cm

We can find the area of sector in 2 methods

Method 1 :

Formula :

${ \rm {\dfrac{\pi {r}^{2} \theta }{360} }}$

Here , r is radius & θ is the angle in sector where θ is measured in degrees

${ \rm{ \dfrac{\pi \times 3.5 \times 3.5 \times 90}{360} = 9.6 {cm}^{2} }}$

Hence , area of sector = 9.6cm²

Method 2 :

Formula:

${\rm{\dfrac{1}{2} {r}^{2} \theta}}$

Here , r is radius & θ is angle in sector where θ is measured in radians

First we have to convert 90° into radians

We know that π radians = 180°

90 ° = π/2 radians

Substituting

$\frac{1}{2} \times 3.5 \times 3.5 \times \frac{\pi}{2} = {\rm {9.6 {cm}^{2} }}$

Hence , area of sector = 9.6 cm²