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Areas Related to Circles
NCERT Exemplar Ch 10
CBSE_NCERT_EXEMPLAR_CH10
Grade 10

Question:

A round table cover has six equal designs. If the radius of the cover is $28\text{ cm}$, find the cost of making the designs at the rate of Rs $0.35$ per $\text{cm}^2$. (Use $\sqrt{3} \approx 1.7$)

Step-by-Step Solution

Key Concept: 6 equal designs form 6 minor segments of central angle $\theta = 60^\circ$. Area of 1 design $= \text{Sector area}(60^\circ) - \text{Area of equilateral } \Delta$.
Stepwise Solution:

Central angle $\theta = 360^\circ / 6 = 60^\circ$. Radius $r = 28\text{ cm}$. [1.0 Mark]

Area of 1 sector $= \dfrac{60}{360} \times \dfrac{22}{7} \times 28 \times 28 = \dfrac{1}{6} \times 2464 = 410.67\text{ cm}^2$. [1.0 Mark]

Area of 1 equilateral $\Delta = \dfrac{\sqrt{3}}{4} \times 28 \times 28 = 1.7 \times 7 \times 28 = 333.2\text{ cm}^2$. [1.0 Mark]

Area of 1 design $= 410.67 - 333.2 = 77.47\text{ cm}^2$.
Total area of 6 designs $= 6 \times 77.47 = 464.82\text{ cm}^2$. [1.0 Mark]

Total cost $= 464.82 \times 0.35 = \text{Rs } 162.68$. [1.0 Mark]

Marking Scheme:

• Finding central angle $60^\circ$ and 1 sector area: 1.0 Mark
• Finding 1 triangle area $= 333.2\text{ cm}^2$: 1.0 Mark
• Area of 1 design $= 77.47\text{ cm}^2$: 1.0 Mark
• Total area of 6 designs $= 464.82\text{ cm}^2$: 1.0 Mark
• Calculating cost $=$ Rs 162.68: 1.0 Mark

Correct Answer:
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