The diagram shows a fountain at the center of a circular park. The radius of the circle is 30 ft. The circular region is divided into six equal parts. What is the length of the arc in the shaded region? Round to the nearest tenth.
A circle is divided into 6 equal slices. A circle in the center is labeled, fountain. One of the slices is shaded and labeled, one-sixth.
60 ft
Of course we can't see what part is shaded, so the bot's answer
is meaningless
Lol.
To find the length of the arc in the shaded region, we need to calculate the circumference of the entire circle and then find one-sixth of it.
1. First, let's find the circumference of the circle. The formula to calculate the circumference is C = 2πr, where C is the circumference and r is the radius. In this case, the radius is given as 30 ft. So, the circumference is C = 2π(30) = 60π ft.
2. Now that we have the circumference of the entire circle, we need to find one-sixth of it. Since the circular region is divided into six equal parts, each part will have the same measure. Therefore, the length of the arc in the shaded region will be one-sixth of the circumference.
One-sixth of the circumference = (1/6) * 60π = 10π ft.
3. Finally, we can approximate the value of π to the nearest tenth as 3.14 and calculate the length of the arc in the shaded region.
Length of the arc in the shaded region ≈ 10π ft ≈ 10 * 3.14 ft ≈ 31.4 ft (rounded to the nearest tenth).
So, the length of the arc in the shaded region is approximately 31.4 ft.