Question

The radius of a circle is 18 cm the ark of the circle subtends an angle of 75° at the center of the circle what is the length of the

Answer 1

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Answer 2

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Answer 3

To find the length of the arc of a circle, you can use the formula:

\[
\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r
\]

where:
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.

Given:
- The radius \(r = 18\) cm,
- The angle \(\theta = 75^\circ\).

Now, plug in the values:

\[
\text{Arc Length} = \frac{75}{360} \times 2\pi \times 18
\]

First, simplify the fraction:

\[
\frac{75}{360} = \frac{5}{24}
\]

Now calculate the arc length:

\[
\text{Arc Length} = \frac{5}{24} \times 2 \times \pi \times 18
\]

Calculate \(2 \times 18 = 36\):

\[
\text{Arc Length} = \frac{5}{24} \times 36\pi
\]

Now simplify:

\[
\text{Arc Length} = \frac{5 \times 36\pi}{24}
\]

Divide \(36\) by \(24\):

\[
\frac{36}{24} = 1.5
\]

Thus, the expression becomes:

\[
\text{Arc Length} = 5 \times 1.5\pi = 7.5\pi
\]

Finally, use \(\pi \approx 3.14\) to calculate a numerical approximation:

\[
\text{Arc Length} \approx 7.5 \times 3.14 \approx 23.49 \, \text{cm}
\]

So, the length of the arc is approximately \(23.49\) cm.

Answer 4

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Answer 5

I'm glad to hear that the answer was correct! 🎉 If you have any more questions or if there's anything else you'd like to discuss, just let me know! 😄💯