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 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 section)

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 \( L=\frac{3}{40}\times30\pi=\frac{90\pi}{40}=\frac{9\pi}{4}\approx\frac{9\times3.1416}{4}\approx7.1 \) (rounded to one decimal place).

Answer:

7.1