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Ayushree

Asked: September 23, 2026In: Class 9 Maths

In my school, the playground is too small to have a 400 m track, so the school constructed a 200 m track instead. Does this mean that we need a smaller stagger for the race tracks in my school (i.e., smaller than the stagger used in the Olympics), for the same 4 x 100 m relay race?

No, a larger stagger is needed. In a 400 m race, runners navigate two bends on a 400 m track but four bends on a 200 m track, requiring twice the total stagger distance.

Ayushree

Asked: September 23, 2026In: Class 9 Maths

Fig. 6.53 shows two circles passing through each other’s centres. Find the area of the region enclosed by the two circles in terms of the common radius r.

The intersection of the circles consists of two 120° sectors minus two equilateral triangles of side r, giving overlapping area (2π/3 – √3/2)r². The total union area equals 2πr² minus this overlap: (4π/3 + √3/2)r².

Ayushree

Asked: September 23, 2026In: Class 9 Maths

In Fig. 6.51 we see two concentric circles with a common centre O. A chord BC of the larger circle is drawn, touching the smaller circle at A. The length of BC is l. Show that the area of the green region enclosed between the two circles is (1/4)pi l².

Radius OA is perpendicular to tangent BC, bisecting it into segments of length l/2. In right-angled triangle OAB, R² – r² = (l/2)² = l²/4. The ring area is pi(R² – r²) = (1/4)pi l².

Ayushree

Asked: September 23, 2026In: Class 9 Maths

In Fig. 6.50, four semicircles have been drawn within the given square whose side is 2 units. The centres of these semicircles are the midpoints of the sides. They create a 4-petalled flower (shown in blue). Find the perimeter and the area of this flower.

Semicircles have diameter 2, radius 1. Perimeter consists of 4 full semicircular arcs totaling 4 x (pi x 1) = 4pi units. Flower area equals 4 semicircles minus the square: 2pi – 4 units².

Kriti

Asked: September 21, 2026In: Class 9 Maths

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?

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 ...

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In my school, the playground is too small to have a 400 m track, so the school constructed a 200 m track instead. Does this mean that we need a smaller stagger for the race tracks in my school (i.e., smaller than the stagger used in the Olympics), for the same 4 x 100 m relay race?

Fig. 6.53 shows two circles passing through each other’s centres. Find the area of the region enclosed by the two circles in terms of the common radius r.

In Fig. 6.51 we see two concentric circles with a common centre O. A chord BC of the larger circle is drawn, touching the smaller circle at A. The length of BC is l. Show that the area of the green region enclosed between the two circles is (1/4)pi l².

In Fig. 6.50, four semicircles have been drawn within the given square whose side is 2 units. The centres of these semicircles are the midpoints of the sides. They create a 4-petalled flower (shown in blue). Find the perimeter and the area of this flower.

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?

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