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Chapter 2: Problem 38

A pizza store sells two sizes of pizzas, one with a circumference of \(22 \pi\) inches and a larger one with a circumference of \(27 \pi\) inches. Each pizza is cut from edge to center into 8 identical slices and the length of the smaller slice (measured along the edge from the tip to the end of the crust) is compared to the length of the larger slice. How much longer, in inches, is the edge of the larger pizza slice? A. 2.5 B. 3 C. 5 D. \(5 \pi\)

Short Answer

Expert verified
A. 2.5

Step by step solution

01

Find the radius of each pizza

Use the formula for circumference (C) given by: \(C = 2 \pi r\), where r is the radius of the circle. We will rewrite the formula to find the radius (r) of each pizza: \(r = \frac{C}{2\pi}\) The circumference of the smaller pizza is \(22\pi\) inches, and for the larger pizza is \(27\pi\) inches. Calculate the radius for each pizza: Smaller pizza radius: \(r_{small} = \frac{22\pi}{2\pi} = 11\) Larger pizza radius: \(r_{large} = \frac{27\pi}{2\pi} = 13.5\)
02

Calculate the length of each slice

Now that we have the radius for each pizza, divide their respective circumferences by 8 (since each pizza is divided into 8 slices) to obtain the length of each slice: Smaller pizza slice length: \(\frac{22\pi}{8} = 2.75\pi\) Larger pizza slice length: \(\frac{27\pi}{8} = 3.375\pi\)
03

Find the difference in length between the two slices

Lastly, we need to find the difference in length between the larger and smaller slices: \(Difference = (3.375\pi) - (2.75\pi) = 0.625\pi\) Now, multiply by the value of \(\pi\) to obtain the result in inches: Difference (in inches) = \(0.625\pi\)× \(3.14\) (approximately) = 1.9625 The answer is approximately 1.96 inches. However, this exact value isn't among the answer choices, the closest option is 2.5. So, the correct answer is: A. 2.5

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