Question
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The formula for the circumference of a circle is C = pi. d, where C = circumference and d = diameter. It can also be
defined as C = 2 pi. r, where r = radius. If 360 degrees = 2 pi. radians, and the formula for arc length is 0 = s/r, then
determine the length created by a 60-degree central angle in a circle with a 2-inch diameter and explain how you found it.
Answer in 3 sentences in a 5th graders response
The formula for the circumference of a circle is C = pi. d, where C = circumference and d = diameter. It can also be
defined as C = 2 pi. r, where r = radius. If 360 degrees = 2 pi. radians, and the formula for arc length is 0 = s/r, then
determine the length created by a 60-degree central angle in a circle with a 2-inch diameter and explain how you found it.
Answer in 3 sentences in a 5th graders response
Answers
GPT-4o mini
To find the length of the arc created by a 60-degree angle in a circle with a 2-inch diameter, we first need to find the radius, which is half of the diameter. So, the radius is 1 inch. Then, we use the arc length formula \( s = \frac{\theta}{360} \times C \), where \( C \) is the circumference calculated as \( C = \pi \times d = \pi \times 2 \) inches, giving us about 6.28 inches. Now we can find the arc length by multiplying \( \frac{60}{360} \) by \( 6.28 \), which equals about 1.05 inches.