Question

the area of the sector of a circle of radius r/2 and central angle 2 theta is​

Answer 1

Answer:

pi*theta*r/720

Step-by-step explanation:

let the radius of a circle be r and central angle of one of its sectors be theta.

we know, area(sector)=theta/360*pi*r^2

                                    =(2Q*pi*r^2)/(360*4)

                                     =Q*pi*r/720                               [let Q=theta]

Answer 2

Answer:

The Area of the sector of circle with radius $\dfrac{r}{2}$ and central angle 2 Ф  is $\dfrac{\Pi \times r^{2}\times \ \Theta }{720^{\circ}}$

Step-by-step explanation:

Given as :

The radius of the circle = $\dfrac{r}{2}$

The central angle = 2 Ф

Let The Area of the sector of circle = A

According to question

∵ Area of the sector of circle = $\frac{\Pi \times radius^{2}\times \Theta }{360^{\circ}}$

Or, A = $\dfrac{\Pi \times r^{2}\times \Theta }{360^{\circ}}$

Or, A = $\dfrac{\Pi \times (\frac{r}{2})^{2}\times \ 2\Theta }{360^{\circ}}$

Or, A = $\dfrac{\Pi \times r^{2}\times \ \Theta }{720^{\circ}}$

So, The Area of the sector of circle = A = $\dfrac{\Pi \times r^{2}\times \ \Theta }{720^{\circ}}$

Hence, The Area of the sector of circle with radius $\dfrac{r}{2}$ and central angle 2 Ф  is $\dfrac{\Pi \times r^{2}\times \ \Theta }{720^{\circ}}$     Answer