Calculate the area other than the area common between two quadrants of circles of radius 8 cm each

Calculate the area of the designed region in the given figure common between the two quadrants of circles of radius 8 cm each. [Use Π = 22/7]

The designed area is the common region between two sectors BAEC and DAFC.

Area of sector BAEC = `90^@/360^@ xx 22/7xx(8)^2`

`=1/4xx22/7xx64`

`=(22xx16)/7 cm^2`

`= 352/7 cm^2`

Area of ΔBAC = `1/2xxBAxxBC`

`= 1/2xx8xx7 = 32 cm^2`

Area of the designed portion = 2 × (Area of segment AEC)

= 2 × (Area of sector BAEC − Area of ΔBAC)

`= 2xx(352/7 - 32) = 2((352-224)/4)`

`= (2xx128)/7`

`= 256/7 cm^2`

Concept: Areas of Combinations of Plane Figures

  Is there an error in this question or solution?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Solution:

We use the formula for the area of sectors of the circle and the area of the square to solve the problem.

In a circle with radius r and the angle at the centre with degree measure θ,

Area of a sector = θ/360° × πr2

Area of a quadrant = 90°/360° × πr2 = 1/4 πr2

Area of plain or unshaded part of the square = Area of square - Area of quadrant 

= side2 - (1/4 × πr2)

= (8 cm × 8 cm) - (1/4 × 22/7 × 8 cm × 8 cm)

= 64 cm2 - 352/7 cm2

= 96/7 cm2

Area of the designed region = Area of the quadrant - Area of plain or unshaded part of the square

= (1/4 × 22/7 × 8 cm × 8 cm) - 96/7 cm2

= 352/7 cm2 - 96/7 cm2

= 256/7 cm2

☛ Check: NCERT Solutions for Class 10 Maths Chapter 12

Video Solution:

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.3 Question 16

Summary:

The area of the designed region common between the two quadrants of circles of radius 8 cm each is 256/7 cm2.

☛ Related Questions:

Math worksheets and
visual curriculum