Question

type the correct answer in the box. use numerals instead of words. a circular pool has a diameter of 30 feet. a section of the top railing with a central angle of 27° is broken and needs to be replaced. what approximate length of railing needs to be replaced? round your answer to one decimal place. about \boxed{} feet of railing needs to be replaced.

Explanation:

Step1: Find the circumference of the circle

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter. Given \( d = 30 \) feet, so \( C=\pi\times30 = 30\pi \) feet.

Step2: Calculate the length of the arc (railing)

The length of an arc is given by the formula \( L=\frac{\theta}{360^\circ}\times C \), where \( \theta \) is the central angle. Here, \( \theta = 27^\circ \) and \( C = 30\pi \). So \( L=\frac{27^\circ}{360^\circ}\times30\pi \).
First, simplify \( \frac{27}{360}=\frac{3}{40} \). Then \( L=\frac{3}{40}\times30\pi=\frac{90\pi}{40}=\frac{9\pi}{4}\approx\frac{9\times3.1416}{4}\approx7.0686 \). Rounding to one decimal place, we get \( 7.1 \).

Answer:

7.1