Question

9. The figure 17.30 consists of four small semi-circles
of equal radii (each 42 cm) the perimeter of the
shaded region is
(a) 524 cm
(c) 396 cm
(6) 264 cm
(d) 504 cm​

Answer 1

Answer:

radii of small semicircles are given ,

r = 42 cm => d = 84 cm

so radius of bigger semicircle.

R = 84 cm

Substitute in the perimeter formula,

Perimeter of 2 semicircle = 2 × πr + 2r

= 2 × 22 × 84 + 2 × 84

= 44 × 84/7 + 168

and then you will arrive at the answer...

Answer 2

Perimeter of one smaller semicircular shaded region ↓

$\huge = > \frac{ \text{Perimeter of circle}}{2} \\ \\ \huge = > \frac{2\pi r}{2} \\ \\ \huge= > \pi r \\ \\ \huge = > \frac{22}{7} \times 42 \\ \\ \huge= > (22 \times 6 ) \\ \\ \huge= > 132 \: \: \rm cm$

Actual perimeter of smaller semicircular region =

$\huge = > 132 - 84 \\ \\ \huge = > 48 \ \: \rm cm$

And,

Perimeter of larger semicircular region ↓↓

$\huge = > \pi r \\ \\\huge = > \frac{22}{7} \times 84 \\ \\ \huge= > 22 \times 12 \\ \\ \huge= > 264 \: \: \rm cm$

Excluded measure in larger semicircular shaded region = 84 cm

Actual perimeter of larger semicircular shaded region →

$\huge = > (264 - 84 )+ (132 - 84) \\ \\ \huge = > 180 + 48 \\ \\ \huge= > 228 \: \: \rm{}cm$

Now, Required perimeter =

$\huge = > (2 \times 48) +( 2 \times 228) \\ \\ \huge= > 96 + 456 \\ \\\huge = > 552 \: \rm cm$