Each circle of diameter d sits in a square cell of area d². The ratio of circle area to each cell is (π / 4)d² / d² = π / 4. Both figures have covered fraction π / 4 approximately 11/14 (approx 78.5%).
Fig. 6.45: What fraction of the rectangle is covered by the circles? Fig. 6.46: What fraction of the rectangle is covered by the circles?
Share
Let the diameter of each circle be d = 2r.
In Fig. 6.45, there are 3 identical circles in a rectangle of dimensions 3d x d.
Total area of rectangle = 3d x d = 3d².
Total area of 3 circles = 3 x πr² = 3 x π(d/2)² = 3 x (π / 4)d².
Fraction covered = [3 x (π / 4)d²] / [3d²] = π / 4.
Using π approximately 22/7, fraction = (22/7) / 4 = 11/14 approximately 0.785 (or 78.5%).
In Fig. 6.46, there are 4 identical circles in a rectangle of dimensions 4d x d.
Fraction covered = [4 x (π / 4)d²] / [4d²] = π / 4 approximately 11/14 approximately 0.785.
Both give π / 4.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/