Question

a sector of a circle of radius r cm containing an angle theta. the area of sector is A cm square and perimeter of sector is 50 cm. prove that 1) theta = 360/pi(25/r - 1)

Answer 1

Answer:

$a) \theta=\dfrac{360^{\circ}}{\pi}(\frac{25}{r}-1)$

$b) A=25r-r^2$

Hence Proved

Step-by-step explanation:

A sector of a circle of radius r cm

Angle of sector is $\theta$

Formula: $l=r\theta$

Perimeter of sector is 50 cm

$l+r+r=50$

$r\theta+2r=50$

$\theta =\dfrac{50-2r}{r}$

$\theta=2(\frac{25}{r}-1)$

Change into degree

(a)

$\theta =\dfrac{180^{\circ}}{\pi}2(\frac{25}{r}-1)$

$\theta=\dfrac{360^{\circ}}{\pi}(\frac{25}{r}-1)$

Hence Proved

(b)

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

Area of sector $=\dfrac{360^{\circ}}{360\times \pi}(\frac{25}{r}-1)\pi r^2$

Area of sector, $A=25r-r^2$

Hence Proved

Answer 2

Answer:

Plsss mark it as brainliest