Question

The area of a circle with centre O is 308 cm2 . Find the perimeter of the
shaded semicircle from the following figure.

1}72 cm
2}58 cm
3}108 cm
4}36√2 cm

Answer 1

The perimeter of shaded semicircle is $22\sqrt{2} \ m$

Step-by-step explanation:

Given,

Area of the circle$=308m^{2}$

We know area of a circle is given $\pi r^{2}$

So,

$\pi r^{2}=308$

⇒$r^{2}=\frac{308}{\pi}$

⇒$r=\sqrt{98}$

⇒$r=7\sqrt{2} \ m$

∴Perimeter of the shaded semicircle is equal to perimeter of half of the circle.

So,

Perimeter of the shaded semicircle$=\pi r$

                                                          $=\pi \times 7\sqrt{2}$

                                                         $=22\sqrt{2} \ m$

So, The perimeter of shaded semicircle is $22\sqrt{2} \ m$

Answer 2

Answer:

36$\sqrt{2}$

Step-by-step explanation:

Area of Circle = π$r^{2}$

∴ π$r^{2}$ = 308$cm^{2}$

∴ $\frac{22}{7}$ x $r^{2}$ = 308$cm^{2}$

∴ $r^{2}$ = 7$\sqrt{2}$

Perimeter of Semi-Circle =  πr + d (r = 7$\sqrt{2}$, d = 2r = 14$\sqrt{2}$)

∴ πr + d = $\frac{22 *7\sqrt{2} }{7}$ + 14$\sqrt{2}$  (7 and 7 get cancelled)

∴ 22$\sqrt{2}$ + 14$\sqrt{2}$ = 36$\sqrt{2}$