Question

Two semicircles of equal radii are cut out of a semicircle piece of cardboard.Find the area of the shaded portion.(Ans=38.5m^square)​

Answer 1

Given :

• Radius of bigger Circle (R) is 14 m
• And two semicircles are removed from circle as shown in figure.

To FinD :

• Area of the remaining portion

Solution :

For finding area of remaining Portion, We have to find out area of the bigger semicircle and then we have to remove area of small circles.

• Radius of Small semicircles (r) = 3.5 m

So, Area of Bigger Semi Circle

⇒Area = πR²/2

⇒Area = [(22/7) * (7)²]/2

⇒Area = (49 * 22)/ 7 * 2

⇒Area = 1078/14

⇒Area = 77

∴ Area of Bigger Semicircle is 77 m²

__________________________

Now, we have to find area of small semicircles. As they are two semicircle. So, we can multiply area of 1 semicircle by 2.

⇒Area of Semicircles = 2 * (πr²) / 2

⇒Area of semicircles = πr²

⇒Area = (22/7) * (3.5)²

⇒Area = (22/7) * 12.25

⇒Area = (12.25 * 22)/7

⇒Area = 269.5/7

⇒Area = 38.5

∴ Area of Two Semicircles is 38.5 m²

______________________

⇒Area of Shaded Portion = 77 - 38.5

⇒Area of shaded portion = 38.5

∴ Area of Shaded Portion is 38.5 m² (approx.)

Answer 2

Answer :

Given -

• Big semicircle has diameter of 14 m.
• Two small semicircles of radius 7 m is cut out from big semicircle.

To Find -

• Shaded area ?

Answer :

We need to find the area of big semicircle and then subtract the area of both the small semicircles.

Area of the big semicircle = πr²/2.

⇒ (22/7*7²)/2

⇒ (22*7)/2

⇒ 11*7

⇒ 77 m²

Now, Area of one semicircle = πr²/2.

⇒ (3.14*(3.5)²)/2

⇒ (3.14*12.25)/2

⇒ (38.46)/2

⇒ 19.23

So, Area of both the semicircles = 19.23*2 = 38.46 m².

Now, Finding the area of shaded portion = 77 - 38.46 = 38.54 m².

Hence, Area of Shaded portion = 38.54 m².