/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 26 Suppose a slice of a 10 -inch pi... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 26

Suppose a slice of a 10 -inch pizza has an area of 15 square inches. What is the angle of this slice?

Short Answer

Expert verified
The angle of the pizza slice is approximately \(68.75\) degrees.

Step by step solution

01

Write down the given information

We are given the area of the slice A = 15 square inches and the radius of the pizza r = 10 inches/2 = 5 inches.
02

Set up the formula for the area of a sector

The formula for the area of a sector is A = (1/2) * r^2 * 胃, where A is the area, r is the radius, and 胃 is the angle of the sector in radians. We will plug in the values of A and r and solve for 胃.
03

Insert the values into the formula and solve for 胃

15 = (1/2) * (5^2) * 胃 Multiplying both sides by 2: \(30 = 25 * 胃\) Divide by 25: \(\displaystyle 胃 = \frac{30}{25}\) Simplify: \(\displaystyle 胃 = \frac{6}{5}\) radians
04

Convert radians to degrees

To convert radians to degrees, we can use the formula: Degrees = Radians * \(\displaystyle\frac{180}{蟺}\) So, \(\displaystyle 胃 = \frac{6}{5} * \frac{180}{蟺}\) By multiplying: \(胃 = \frac{1080}{5蟺}\) degrees
05

Calculate the value of the angle

Now, we will find the approximate value of the angle: \(\displaystyle 胃 鈮� \frac{1080}{5 * 3.1416}\) \(胃 鈮� \frac{1080}{15.708}\) \(胃 鈮� 68.75\) degrees The angle of the pizza slice is approximately 68.75 degrees.

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