The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\...
Question 1 Report
The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\)
Answer Details
To find the radius of the circle, we need to use the formula:
$$
\text{length of arc} = \theta \frac{\pi r}{180}
$$
where $\theta$ is the angle subtended by the arc at the center of the circle, $r$ is the radius of the circle, and $\pi$ is the mathematical constant pi.
Substituting the given values, we get:
$$
50 = 75 \times \frac{\pi r}{180}
$$
Simplifying the equation, we get:
$$
r = \frac{50 \times 180}{75 \times \pi} \approx 38.2 \text{ cm (to 3 significant figures)}
$$
Therefore, the correct answer is 38.2cm.
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