Questions: Find the circumference of a circle if the area is 300 square centimeters. A) 61.38 cm B) 56.25 cm C) 84.74 cm D) 9.77 cm

Find the circumference of a circle if the area is 300 square centimeters. A) 61.38 cm B) 56.25 cm C) 84.74 cm D) 9.77 cm
Transcript text: Find the circumference of a circle if the area is 300 square centimeters. A) 61.38 cm B) 56.25 cm C) 84.74 cm D) 9.77 cm
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Solution

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Solution Steps

To find the circumference of a circle given its area, we can use the following steps:

  1. Use the formula for the area of a circle, \( A = \pi r^2 \), to solve for the radius \( r \).
  2. Once the radius is found, use the formula for the circumference of a circle, \( C = 2 \pi r \), to find the circumference.
Step 1: Calculate the Radius from the Area

Given the area of the circle \( A = 300 \) square centimeters, we use the formula for the area of a circle: \[ A = \pi r^2 \] Solving for the radius \( r \): \[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{300}{\pi}} \approx 9.772 \text{ cm} \]

Step 2: Calculate the Circumference from the Radius

Using the radius \( r \approx 9.772 \) cm, we can find the circumference \( C \) using the formula: \[ C = 2 \pi r \] Substituting the value of \( r \): \[ C = 2 \pi \times 9.772 \approx 61.40 \text{ cm} \]

Final Answer

The circumference of the circle is: \[ \boxed{61.40 \text{ cm}} \] The answer is A.

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