A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure.

Based on the above information, answer the following questions :

Circle diagram with 5 diameters drawn through the centre, dividing the circle into 10 equal pie-slice sectors, illustrat — Fig. for Q52

Areas Related to Circles

Areas Related to Circles — Case Study (Silver Brooch)

Official Answer

No marks are attached to this stem; it only sets up context (circle of diameter 35 cm with 5 diameters forming 10 equal sectors) for the numbered sub-questions that follow. The clean divisibility of 35 by 7 signals that $\pi = \frac{22}{7}$ should be used throughout.

broochsilver wirediametercirclesectorsdiameterscase study

Marking Scheme

1No marks are allocated to this introductory stem; marks are awarded only in the numbered sub-questions Q38(i) and Q38(ii) that follow.

Hint

Since the diameter (35 cm) is a multiple of 7, use $\pi = \frac{22}{7}$ for exact answers throughout this case study.

Quick Oral Answer

This is just the background information for the brooch case study — a circle of diameter 35 cm split into 10 equal sectors by 5 diameters — the actual questions on radius and circumference follow after this.

Analysis & Explanation

Introductory stem of the brooch case study — sets up context and the hint to use $\pi = \frac{22}{7}$ .

Concept

A silver-wire brooch is a circle of diameter 35 cm, further divided by 5 diameters into 10 equal sectors, like spokes of a wheel.
Each sector's central angle = $360^\circ/10 = 36^\circ$ (relevant to later parts).

Key points

$35 = 5 \times 7$ is a deliberate CBSE hint: use $\pi = \frac{22}{7}$ for exact, clean values (not 3.14, which gives messy decimals).

Real-world

Models a physical jewellery design problem, testing fluent conversion between diameter, radius, circumference, and sector measures.

Common Mistakes

1Treating the introductory stem itself as a question requiring a numeric answer, when it is only context for the sub-parts.
2Using $\pi = 3.14$ instead of $\frac{22}{7}$ despite the diameter (35 cm) being a clear multiple of 7.
3Confusing '5 diameters creating 10 sectors' with '10 diameters' — each diameter passes through the centre and creates 2 sectors, so 5 diameters create exactly 10 equal sectors.

Interesting Facts

A real circular brooch divided into 10 equal sectors by 5 diameters mathematically mirrors a 10-spoke wheel design, a motif seen in ancient Indian temple architecture (e.g., the wheel of the Konark Sun Temple).

CBSE frequently sets circle diameters as multiples of 7 (7, 14, 21, 28, 35, 42...) specifically so that the fractional value π = 22/7 yields whole-number or simple-fraction answers, avoiding messy decimals in board exams.

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Frequently Asked Questions

Why is the diameter chosen as 35 cm specifically?

Because 35 is a multiple of 7, using $\pi = \frac{22}{7}$ gives exact, clean values for radius and circumference, which is the standard CBSE convention for such problems.

How many sectors do 5 diameters create?

10 equal sectors, since each diameter divides the circle in half through the centre, and 5 diameters (10 rays from the centre, evenly spaced) create 10 equal 36° sectors.