3. "You'll need to know some geometry to work here," Jocelyn says. "I need you to figure out the volume of this pizza," she says. And she draws this diagram on one of the whiteboards that dot the walls for when patrons want to do physics problems together. It's a circular pizza with radius r and height t.
3. "You'll need to know some geometry to work here," Jocelyn says. "I need you to figure out the volume of this pizza," she says. And she draws this diagram on one of the whiteboards that dot the walls for when patrons want to do physics problems together. It's a circular pizza with radius r and height t.
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Work on number 3
![**EXERCISE 2: SCALING PIZZA SIZES**
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**“Scaling problems are also called proportional reasoning problems.** For example, let’s consider the area \(A\) of a rectangle: \(A = LW\), where \(L\) and \(W\) are the dimensions of the rectangle. If you quadruple \(L\) and halve \(W\), then the right-hand side of that equation doubles \([(4)(1/2) = 2]\). If the right-hand side of an equation doubles, then the left-hand side (i.e., \(A\)) must also double.”
3. “You’ll need to know some geometry to work here,” Jocelyn says. “I need you to figure out the volume of this pizza,” she says. And she draws this diagram on one of the whiteboards that dot the walls for when patrons want to do physics problems together. It’s a circular pizza with radius \(r\) and height \(t\).
4. “We want to redo our pricing so that all the pizzas have the same price/area. We are going to price our smallest size pizza – “the Mini” at $5. What should we price our pizza that has twice that diameter (the Medium)? Why don’t you write the formula for the area of a circle and think about what happens to the area if you double the diameter.”
5. Jocelyn says, “I made some balls of dough (ball radius \(R\)) for our Mini pizzas (radius \(r\), thickness \(t\))” and she tosses you a dough ball. “If I wanted to make a “Medium” pizza with the same thickness \(t\), what would
a. The volume of the new pizza be in terms of \(r\) and \(t\)?
b. The radius, \(R_2\), of dough balls (in terms of \(R\)) needed to make those pizzas?”
Below this text, there would typically be an accompanying diagram illustrating a circular pizza with labeled dimensions, including radius \(r\) and height \(t\), to aid in visualizing problem 3’s geometric calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a5bf8ad-4965-4e63-b21c-5c2ad3e92a8d%2Fcc64c135-8d47-4262-8788-cb99b635d41f%2Fdnvw1ab_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**EXERCISE 2: SCALING PIZZA SIZES**
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**“Scaling problems are also called proportional reasoning problems.** For example, let’s consider the area \(A\) of a rectangle: \(A = LW\), where \(L\) and \(W\) are the dimensions of the rectangle. If you quadruple \(L\) and halve \(W\), then the right-hand side of that equation doubles \([(4)(1/2) = 2]\). If the right-hand side of an equation doubles, then the left-hand side (i.e., \(A\)) must also double.”
3. “You’ll need to know some geometry to work here,” Jocelyn says. “I need you to figure out the volume of this pizza,” she says. And she draws this diagram on one of the whiteboards that dot the walls for when patrons want to do physics problems together. It’s a circular pizza with radius \(r\) and height \(t\).
4. “We want to redo our pricing so that all the pizzas have the same price/area. We are going to price our smallest size pizza – “the Mini” at $5. What should we price our pizza that has twice that diameter (the Medium)? Why don’t you write the formula for the area of a circle and think about what happens to the area if you double the diameter.”
5. Jocelyn says, “I made some balls of dough (ball radius \(R\)) for our Mini pizzas (radius \(r\), thickness \(t\))” and she tosses you a dough ball. “If I wanted to make a “Medium” pizza with the same thickness \(t\), what would
a. The volume of the new pizza be in terms of \(r\) and \(t\)?
b. The radius, \(R_2\), of dough balls (in terms of \(R\)) needed to make those pizzas?”
Below this text, there would typically be an accompanying diagram illustrating a circular pizza with labeled dimensions, including radius \(r\) and height \(t\), to aid in visualizing problem 3’s geometric calculations.
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