Question

Find the area of the minor segment of a circle of radius 42cm, if length of the corresponding arc is 44cm

Answer 1

r = 42cm
area = πr²
= 22/7×42×42
= 22×6×42
= 5544cm²
angle be x, now
angle of the arc = x/360 × 264
44×360 = 264x
x = 60°

area of the sector = 60/360 × 5544
= 924cm²

Answer 2

Answer: 924 square cm.

Step-by-step explanation:

Since, Arc length = Radius × Central angle,

Here the radius = 42 cm,

Arc length = 44 cm,

⇒ 44 = 42 × Central angle,

⇒ $\text{ Central angle } = \frac{44}{42}\text{ Radian}$

Since,

$\pi\text{ radian} = 180^{\circ}$

⇒ $\text{ 1 Radian} = \frac{180^{\circ}}{\pi}$

⇒ $\frac{44}{42}\text{ radian}=\frac{44}{42}\times \frac{180\times 7}{22}=60^{\circ}$

Thus, the area of the segment that makes central angle of 60° is,

$A=\frac{60^{\circ}}{360^{\circ}}\pi (42)^2$

$=\frac{1}{6}\times\frac{22}{7}\times 1764$

$=\frac{38808}{42}$

$=924$ square cm.