Question

Three semicircles each of diameter 3 cm a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure.Find the are of shaded region.

Answer 1

Hey Mate!!!

Area of 1st circle = 22/7 × 4.5/2 × 4.5/2 × = 15.9 cm^2

Area of 2nd circle = 22/7 × 3/2 × 3/2 × 1/2 = 3.53

Area of such 3 circles = 3.53 × 2 =7.06
Area of big half circle = 22/7 × 4.5 ×4.5 ×1/2
=31.8

Area of shaded region =
31.8 - ( 3.53 + 7.06)

31.8 - 10.59
17.6 cm^2 + 3.53
= 21.1 cm^2
Please don't refer to the above attatchment

Answer 2

DIAMETER OF SEMICIRCLE = 3CM

RADIUS OF SEMICIRCLE = D/2 = 3/2 = 1.5CM

AREA OF SEMICIRCLE = 1/2πR² = 1/2×22/7×1.5×1.5 = 49.5/14 = 3.53 CM²

AREA OF THREE SEMICIRCLE = 3×3.53 = 10.59 CM².

DIAMETER OF CIRCLE = 4.5CM

RADIUS OF CIRCLE = D/2 = 4.5/2 = 2.25 CM


AREA OF CIRCLE = πR² = 22/7×2.25×2.25 = 111.375/7 = 15.91 CM².

AREA OF BIG SEMICIRCLE = DIAMETER OF THERE SMALL SEMICIRCLE = 3+3+3 = 9CM.

RADIUS OF BIG SEMICIRCLE = D/2 = 9/2 = 4.5 CM.

AREA OF BIG SEMICIRCLE = πR² =22/7×4.5×4.5 = 445.5/7 = 63.64 CM².


AREA OF SHADED REGION = AREA OF BIG SEMICIRCLE - (AREA OF CIRCLE+ 2×AREA OF SMALL SEMICIRCLE)+ AREA OF SEMICIRCLE.


AREA OF SHADED REGION = 63.64-(15.91+2×3.53) + 3.53 = 63.64-22.97+3.53 = 67.17-22.97 = 44.2 Ans.

Hence,

THE AREA OF SHADED REGION = 44.2 CM²