Exercise 37 Page 608

Practice makes perfect

a First, we remember that the area of a circle is given by A=π r^2 and that the diameter is twice the radius. With this information, let's compute the radius of a 12-inch diameter pizza.

12 = 2r ⇒ r = 12/2 = 6 Next, we find the area of this pizza.

A = π(6)^2 ⇒ A = 36π in^2 According to the given information, this pizza is enough for three people. By dividing this area by 3, we will find how much pizza is enough for each person. 36π/3 = 12π in^2 Now we want to buy pizzas for 8 people, so the amount of pizza needed is 8* 12π or 96π in^2. Let's find the area of the pizzas of different sizes.

Diameter (in)	Radius (in)	Area (in^2)	Cost ($)
10	5	P_1 = 25π	6.99
14	7	P_2 = 49π	12.99

Next, let's consider the different ways of buying the pizzas so that it is enough for the 8 people.

Pizzas Required	Amount of Pizza (in^2)	Cost ($)
4 small pizzas	100π	27.96
2 small pizzas and 1 large	99π	26.97
2 large pizzas	98π	25.98

As we can see, in order to spend as little money as possible we must buy two 14-inch pizzas.

b In Part A, we concluded that 8 people can eat with 96π in^2 of pizza. We also found the area of each pizza.

Size	Area (in^2)	Cost ($)
Small	P_1 = 25π	6.99
Large	P_2 = 49π	12.99

In this part we want to buy three pizzas. In the following table, we will write different ways to do it with the total costs.

Number of Pizzas	Area (in^2)	Cost ($)	Enough Pizza?
3 small	75π	20.97	No
2 small and 1 large	99π	26.97	Yes
1 small and 2 large	123π	32.97	Yes
3 large	147π	38.97	Yes

The first option is the cheapest one, but it will not be enough pizza for the 8 people. Therefore, we conclude that the second option is the cheaper one.

c Since we want as much of the thick outer crust as possible, we will start by computing the circumference of each type of pizza. For this, we will use the formula C=2π r.

Size	Radius	Circumference
Small	5	C_1 = 2π(5) = 10π
Large	7	C_2 = 2π(7) = 14π

Let's write some options we have to buy enough pizzas for the 8 people along with the total circumference.

Number of Pizzas	Area (in^2)	Circumference (in)
4 small	100π	40π
2 small and 1 large	99π	34π
1 small and 2 large	123π	38π
2 large	98π	28π

From the options in the table above, we can see that the option that gives as much of the thick outer crust as possible is the first one.

Subchapter links

Communicate Your Answer p.601

Monitoring Progress p.602-605

Exercise 37 Page 608

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