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Areas Related to Circles
NCERT Exemplar Ch 10
CBSE_NCERT_EXEMPLAR_CH10
Grade 10

Question:

An umbrella has $8$ ribs which are equally spaced. Assuming umbrella to be a flat circle of radius $45\text{ cm}$, find the area between the two consecutive ribs of the umbrella.

Step-by-Step Solution

Key Concept: 8 ribs divide the circle into 8 equal sectors. Central angle $\theta = 360^\circ / 8 = 45^\circ$.
Stepwise Solution:

Angle of each sector $\theta = \dfrac{360^\circ}{8} = 45^\circ$. Radius $r = 45\text{ cm}$. [1.0 Mark]

Area $= \dfrac{45}{360} \times \pi r^2 = \dfrac{1}{8} \times \dfrac{22}{7} \times 45 \times 45 = \dfrac{11 \times 2025}{28} = \dfrac{22275}{28}\text{ cm}^2$. [2.0 Marks]

Marking Scheme:

• Finding angle $\theta = 45^\circ$: 1.0 Mark
• Evaluating sector area $= 22275/28\text{ cm}^2$: 2.0 Marks

Correct Answer:
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