Question

2. From a rectangular sheet.four comers in the form of quarter
circles are cut off. A circle from the centre is also cut ott
the radii of all the circles is 1 em and the rectangle measures
8 cm by 5 cm, find the area of the sheet remaining atter all
the pieces are cut off.

Hint: Area of the remaining sheet = Area of rectangular
sheet - Area of the circle -
4x Area of quarter circles​

Answer 1

Step-by-step explanation:

Answer

⇒ Here a=8cm

⇒ Area of square =a

2

=(8)

2

=64cm

2

⇒ Here radius of circle R=4.2cm

⇒ Area of of circle =πR

2

=

7

22

×(4.2)

2

∴ Area of of circle =55.44cm

2

⇒ Radius of sector r=1.4cm and θ=90

o

⇒ Area of 2 sectors =2×

360

o

θ

πr

2

⇒ Area of 2 sectors =2×

360

o

90

o

×

7

22

×(1.4)

2

∴ Area of 2 sectors =3.08cm

2

⇒ Area of shaded region = Area of square - ( Area of circle +Area of 2 sectors)

⇒ Area of shaded region =64−(55.44+3.08)

∴ Area of shaded region =64−58.52=5.48cm

2