An arc of a circle subtends an angle of 75° at the centre of the circle. If the diameter of the circle is 7cm, what Is the length of the arc? (take π = 3.142)
To find the length of the arc, we use the formula:
\(\text{Length of arc} = \frac{\theta}{360^\circ} \times 2\pi r\)
Given:
\(\theta = 75^\circ \)
Diameter = 7cm, r = \(\frac{7}{2}\) = 3.5 cm.
\(\pi = \frac{22}{7}\)
Calculate the circumference of the circle:
\(\text{Circumference} = 2\pi r = 2 \times \frac{22}{7} \times 3.5\)
Calculating:
\(= 2 \times \frac{22}{7} \times \frac{7}{2} = 22 \text{ cm}\)
Calculate the length of the arc:
\(\text{Length of arc} = \frac{75}{360} \times 22\)
Calculating:
\(= \frac{75 \times 22}{360} = \frac{1650}{360} \approx 4.5833 \text{ cm}\)
The length of the arc is approximately 4.58 cm
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