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

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 2

Noooooooo ooooooooooooooooooooooo...,,.........

Answer 3

It seems like there might have been some confusion or frustration with the previous response. How can I help clarify or correct the information for you? Please let me know what specific part you would like to address.

Answer 4

That's the correct answer bruh 😁😁💯💯 ahhhhhhhahh

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! 😄💯