Question

The area of the shaded region is 20 cm2. Find the value of x, correct to 3 significant figures.

Answer 1

Answer-Correct option is

D

154cm2

Area of the shaded region = Area of circle with center at O - Area of semicircle with center at O-Area of smaller semicircle with radius r′-Area of smaller semicircle with radius r′

Here, r=228=14

           r′=2r

           =>r′=214

           =>r′=7

Area of the shaded region =πr2−2πr2−2πr′2−2πr′2

       =2πr2−πr′2

       =2π×142−π72

       =2×

Answer 2

Answer:

8.37cm

Step-by-step explanation:

Look at the photo as a sector of a circle.

x in this case is the radius. In fact, both the height and base is the radius.

To find the radius, we need to form an equation. The only info given is with the area of the shaded area which is 20cm^2. We can say that the area of the sector - area of the triangle = the shaded area.

Area of the sector = $\frac{\pi r^{2} }{4}$

Area of triangle= $\frac{1}{2} bh$

Area of the triangle =$\frac{1}{2} x(x)$  = $\frac{x^{2} }{2}$

The area of the triangle is in that way, as the height and base is x ( and x is the radius here!)

So:

$\frac{\pi r^{2} }{4}$ - $\frac{x^{2} }{2}$ $= 20$

Multiply 4 with the whole equation as it is the LCM.

$4( \frac{\pi x^{2} }{4} - \frac{x^{2} }{2} )\\= \pi x^{2} - 2x^{2} = 80$

Simplify:

$\pi x^{2} -2x^{2} =80\\1.142x^{2} =80\\x^{2} =70.1\\ \sqrt{x^{2}} =\sqrt{70.1} \\x = 8.37$

Here is you go! Hope it helps!