Question

the boundary of the shaded region in the given figure consist of three semicircles the smaller being equal. If the diameter of the larger on is 8 cm find
i)Length of the boundary
ii) The area of the shaded region

Answer 1

Answer:

i) 25.1 cm

ii) 12.57 sq cm

Step-by-step explanation:

i) length of boundary= perimeter(large semicircle) + 2perimeter(small semicircles)

= 22/7 x 4 + 2(22/7 x 2)

= 88/7 + 88/7

=176/7

=25.1 cm

ii)area of shaded region= ar(large semicircle-small semicircle) + ar(small semicircle)

=(1/2 x 22/7 x 4 x 4 - 1/2 x 22/7 x 2 x 2) + (1/2 x 22/7 x 2 x 2)

=(88/7 - 44/7) + (44/7)

=44/7 + 44/7

=88/7

=12.57 sq cm