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Chapter 5: Problem 25

Suppose a slice of a 12 -inch pizza has an area of 20 square inches. What is the angle of this slice?

Short Answer

Expert verified
The angle of the pizza slice is approximately 63.39 degrees.

Step by step solution

01

Understanding the problem and writing down known values

We are given the area of a slice of a 12-inch pizza and its radius. Using the sector formula, we aim to find the angle of the pizza slice. The known values are: Area of the slice (A) = 20 square inches Radius of the pizza (r) = 12 inches / 2 = 6 inches
02

Using the formula for the area of a sector

The formula used to find the area of a sector with angle 胃 (in radians) and radius 'r' is given by: A = (1/2) * 胃 * r^2 Our goal is to find the value of 胃. Using the given values, we can rewrite the formula as: 20 = (1/2) * 胃 * 6^2
03

Solving for 胃

Now, solve for 胃: 20 = (1/2) * 胃 * 36 20 = 18胃 Divide both sides by 18: 胃 = 20/18 胃 = 10/9 radians
04

Converting radians to degrees

Finally, we need to convert the angle from radians to degrees. We can do this using the conversion factor (180掳= 蟺 radians): Angle (in degrees) = Angle (in radians) * (180掳 / 蟺) 胃 (in degrees) = (10/9) * (180掳 / 蟺)
05

Calculating the final result

Now, we can calculate the angle of the pizza slice: 胃 (in degrees) 鈮� (10/9) * (180掳 / 3.14159) 胃 (in degrees) 鈮� 63.39掳 Hence, the angle of the pizza slice is approximately 63.39 degrees.

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