Questions: Find the length of arc ABC. Use 3.14 for the value of π. Round to the nearest hundredth of a cm.

Find the length of arc ABC. Use 3.14 for the value of π. Round to the nearest hundredth of a cm.
Transcript text: Find the length of $\operatorname{arc} A B C$. Use 3.14 for the value of $\pi$. Round to the nearest hundredth of a cm .
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Solution

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Solution Steps

Step 1: Identify the Given Information
  • Radius of the circle (r) = 42 cm
  • Central angle (θ) = 270°
  • Value of π = 3.14
Step 2: Formula for Arc Length

The formula to find the length of an arc (L) is: \[ L = \frac{\theta}{360} \times 2\pi r \]

Step 3: Substitute the Given Values

Substitute the given values into the formula: \[ L = \frac{270}{360} \times 2 \times 3.14 \times 42 \]

Step 4: Simplify the Fraction

Simplify the fraction \(\frac{270}{360}\): \[ \frac{270}{360} = \frac{3}{4} \]

Step 5: Calculate the Arc Length

Now, calculate the arc length: \[ L = \frac{3}{4} \times 2 \times 3.14 \times 42 \] \[ L = \frac{3}{4} \times 263.76 \] \[ L = 197.82 \]

Final Answer

The length of arc ABC is approximately 197.82 cm.

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