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Chapter 5: Problem 28

Suppose a slice of pizza with an angle of 1.1 radians has an area of 25 square inches. What is the diameter of this pizza?

Short Answer

Expert verified
The diameter of the pizza is approximately 13.48 inches.

Step by step solution

01

Write down the given values

We are given: - Angle of the pizza slice (胃) = 1.1 radians - Area of the pizza slice (A) = 25 square inches
02

Use the Area of a sector formula to determine the radius

To find the radius (r), use the formula for the area of a sector: A = 0.5 * r^2 * 胃 Substitute the given values into the formula: 25 = 0.5 * r^2 * 1.1 Now, we need to solve for r.
03

Solve for the radius

Rearrange the formula to isolate r: r^2 = \(\frac{25}{(0.5 * 1.1)}\) Divide 25 by the product of 0.5 and 1.1: r^2 = \(\frac{25}{0.55}\) Calculate the quotient: r^2 = 45.45 Now, take the square root of both sides to find r: \(r = \sqrt{45.45}\) Calculate the square root: r 鈮� 6.74 (approximately)
04

Calculate the diameter of the pizza

Finally, we need to find the diameter (D) using the radius (r). The formula for the diameter is: D = 2 * r Substitute the value of r into the formula: D = 2 * 6.74 Calculate the diameter: D 鈮� 13.48 (approximately) So, the diameter of the pizza is approximately 13.48 inches.

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