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📐 Chapter 6: Measuring Space: Perimeter and Area • Exercise Set 6.3

Verified step-by-step solutions for your class notes.

Exercise Set 6.1 4Exercise Set 6.2 4Exercise Set 6.3 3End-of-Chapter Exercises 5All Exercises 16
Q1

Find the area of a sector of a circle with radius 7 cm if the angle of the sector is $60^\circ$.

Answer: Area of sector = $\pi r^2 \times \frac{\theta}{360}$.
Area $= \frac{22}{7} \times 7^2 \times \frac{60}{360} = \frac{22}{7} \times 49 \times \frac{1}{6} = 22 \times 7 \times \frac{1}{6} = \frac{154}{6} = \frac{77}{3} \approx$ 25.67 cm².

Q2

Find the area of a quadrant of a circle whose circumference is 44 cm.

Answer: Circumference $= 2\pi r = 44 \Rightarrow 2 \times \frac{22}{7} \times r = 44 \Rightarrow \frac{44}{7}r = 44 \Rightarrow r = 7$ cm.
A quadrant is a sector with angle $90^\circ$ (or $\frac{1}{4}$ of a circle).
Area of quadrant = $\frac{1}{4}\pi r^2 = \frac{1}{4} \times \frac{22}{7} \times 7^2 = \frac{1}{4} \times 154 = \frac{77}{2} =$ 38.5 cm².

Q3

The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand in 10 minutes.

Answer: In 60 minutes, the minute hand sweeps $360^\circ$.
In 10 minutes, it sweeps $\frac{10}{60} \times 360^\circ = 60^\circ$.
This forms a sector with $r = 7$ cm and $\theta = 60^\circ$.
Area $= \frac{60}{360} \times \frac{22}{7} \times 7^2 = \frac{1}{6} \times 154 = \frac{77}{3} \approx$ 25.67 cm².

12 2 3 6 9 60° 7 cm
In 10 minutes, the 7 cm minute hand sweeps a 60° sector (Area ≈ 25.67 cm²)