Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A square has sides that measure 5 inches. The square is then divided in half vertically and horizontally, creating 4 smaller squares. What would the total perimeter of the 4 smaller squares be (in inches)? A. 5 B. 6.25 C. 25 D. 40

In this excerpt the narrator puts a revolver under the blanket before going to sleep. What characteristic does this action reveal about the narrator? A. fear about being in a rough neighborhood B. exhaustion so extreme that the narrator is too tired to put the revolver away properly C. a naturally violent temper that leads to being armed at all times D. preparation for questionable situations a traveler might encounter

Which of the following equations represents the line that passes through the two given points? A. \(y=2 x-14\) B. \(y=2 x+3\) C. \(y=-x-1\) D. \(y=-x+1\)

One year ago Harold invested $$\$ 24,000$$ in a bank bond that offers \(3 \%\) annual interest. At the same time, Maude invested \(\frac{1}{3}\) that amount in a fund that produced an annual yield of \(8 \%\). At the end of the year, what was the difference between Harold's interest earnings and Maude's gains from her investment yield? A. $$\$ 80$$ B. $$\$ 240$$ C. $$\$ 640$$ D. $$\$ 5,040$$

Scientists use index fossils to identify the times at which unidentified fossils and certain sediments were deposited. They hypothesize that if a particular fossil is found near an index fossil, in the same layer of rock, then the two fossils were likely from the same time period. The shorter the lifespan of the index fossil species, the more precisely scientists are able to correlate that species with a particular era. Therefore, it is not surprising that ideal index fossils are from shortlived, common, and easy-to- identify species. Which of the following is an example of the effective use of index fossils? A. Scientists fix the time that Mesolenellus hyperborea existed in the late Nevadella era, because they find Mesolenellus hyperborea near and in the same level of rock as Limniphacos perspiculum, a recognized index fossil that existed in that period. B. Scientists determine that Mesolenellus hyperborea were probably mud bottom- dwellers, because hyolitha, which existed during the same time period as Mesolenellus hyperborea, were also bottom dwellers. C. Scientists hypothesize that Mesolenellus hyperborea were wiped out by a sudden climate change that occurred at the end of the Devonian period, when many other trilobites were wiped out. D. Scientists determine that Mesolenellus hyperborea did not exist in Iceland, because Petrianna fulmenta, a similar trilobite, did not exist in Iceland.

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free