Question

In given figure the area of shaded region ( is sq. units) isIn given figure the area of shaded region ( is sq. units) is:

(a) 5
^2/
48

(b) 7
^2
/12

(c) 3
^2/
4

(d) 4
^2/
3​

Answer 1

Answer:

∠BAC=70° , ∠BAX=42°

 Now,  

∠BAC=∠BAX+∠XAC

70°=42°+∠XAC

∠XAC=28°

Step-by-step explanation:

Answer 2

Given,

Radius of small circle $\[ = x\]$

Radius of large circle,

$\[\begin{array}{l} = x + \frac{x}{2}\\ = \frac{{3x}}{2}\end{array}\]$

Angle of section, $\[\theta = 30^\circ \]$

Solution,

Calculate the area of shaded region.

Know that area of sector, whose radius is r and angle of sector is $\[\theta \].$

$\[ = \frac{\theta }{{360^\circ }} \times \pi {r^2}\]$

Area of shaded region,

Area of large circle sector - area of small circle sector

$\[ = \frac{\theta }{{360^\circ }} \times \pi {R^2} - \frac{\theta }{{360^\circ }} \times \pi {r^2}\]$

$\[ = \frac{{30^\circ }}{{360^\circ }} \times \pi {\left( {\frac{{3x}}{2}} \right)^2} - \frac{{30^\circ }}{{360^\circ }} \times \pi {x^2}\]$

$\[ = \frac{1}{{12}} \times \pi \left( {\frac{9}{4}{x^2} - {x^2}} \right)\]$

$\[ = \frac{1}{{12}} \times \pi \times \frac{5}{4}{x^2}\]$

$\[ = \frac{{5\pi }}{{48}}{x^2}\]$

Hence the area of sector is $\[\frac{{5\pi }}{{48}}{x^2}\]$ $\[uni{t^2}\]$

The correct option is (a), i.e. $\[\frac{{5\pi }}{{48}}{x^2}uni{t^2}\]$