8. The given figure consists of 4 small semicircles and two big semici

1.	8. The given figure consists of 4 small semicircles and two big semicircles. If thesmalier semicircles are equal in radii and the bigger semicircles are equal in radi,find the perimeter and the area of the shaded portion of the figure, given thatthe radius of each bigger semicircle is 42 cm. (4)
Answer» From the given figure, we can see that there are 2 large shaded semicircle and 2 small shaded semicircle Let R be the radius of large semicircle and r be the radius of small semicircle. Area of large semicircle Area = (piR^2)/2 There are two large semi circle, therefore total area = 2 x (piR^2)/2 = piR^2 Area of small semicircle Area = (pir^2)/2 There are two large semi circle, therefore total area = 2 x (pir^2)/2 = pir^2 Area of shaded region Area = [piR^2 -pir^2] - pir^2 join all the shaded region we get a circle with radius 42 Area of circle with radius 42 = πR^2=22/7 x 42 x 42 = 5544 cm^2

8. The given figure consists of 4 small semicircles and two big semicircles. If thesmalier semicircles are equal in radii and the bigger semicircles are equal in radi,find the perimeter and the area of the shaded portion of the figure, given thatthe radius of each bigger semicircle is 42 cm. (4)

Answer»

From the given figure, we can see that there are 2 large shaded semicircle and 2 small shaded semicircle

Let R be the radius of large semicircle and r be the radius of small semicircle.

Area of large semicircle

Area = (piR^2)/2

There are two large semi circle,

therefore total area = 2 x (piR^2)/2 = piR^2

Area of small semicircle

Area = (pir^2)/2

There are two large semi circle,

therefore total area = 2 x (pir^2)/2 = pir^2

Area of shaded region

Area = [piR^2 -pir^2] - pir^2

join all the shaded region we get a circle with radius 42

Area of circle with radius 42 = πR^2=22/7 x 42 x 42 = 5544 cm^2