Question

mark wants to order a pizza. drag and drop the correct number or phrase into each box to complete the explanation for which is the better deal. round your answer to the nearest cent. use 3.14 for π.
donnies pizza palace
diameter (in.)\tcost ($)
10\t10
16\t20
the 10-inch pizza costs about
¢ per square inch. the 16-inch pizza costs about
¢ per square inch while the
pizza is a better deal.

Explanation:

Step1: Calculate area of 10 - inch pizza

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r = \frac{d}{2}\) ( \(d\) is the diameter). For a 10 - inch pizza, \(d = 10\), so \(r=\frac{10}{2}=5\). Then \(A_{10}=\pi\times5^{2}=25\pi\). Using \(\pi = 3.14\), \(A_{10}=25\times3.14 = 78.5\) square inches. The cost is \(\$10=1000\) cents. The cost per square inch is \(\frac{1000}{78.5}\approx12.74\) cents? Wait, no, wait the options have 0.13 and 0.1. Wait, maybe I messed up units. Wait, cost is in dollars. Let's recalculate with dollars. Cost per square inch for 10 - inch: cost is \(\$10\), area is \(A = \pi(\frac{10}{2})^{2}=25\pi\approx78.5\) square inches. So cost per square inch is \(\frac{10}{78.5}\approx0.127\approx0.13\) dollars per square inch? Wait, no, the question says "¢ per square inch". So convert dollars to cents: \(\$10 = 1000\) cents. So cost per square inch for 10 - inch: \(\frac{1000}{78.5}\approx12.74\) cents? No, the options have 0.13 and 0.1. Wait, maybe I made a mistake. Wait, 10 - inch pizza: diameter 10, radius 5, area \(A = \pi r^{2}=25\pi\approx78.5\) in². Cost is \(\$10\), so cost per square inch in dollars is \(\frac{10}{78.5}\approx0.127\approx0.13\) dollars per square inch, which is 13 cents per square inch? Wait, no, 0.13 dollars is 13 cents. Wait, the 16 - inch pizza: diameter 16, radius 8, area \(A=\pi\times8^{2}=64\pi\approx200.96\) in². Cost is \(\$20 = 2000\) cents. Cost per square inch in cents: \(\frac{2000}{200.96}\approx9.95\approx10\) cents? No, in dollars: \(\frac{20}{200.96}\approx0.0995\approx0.1\) dollars per square inch. Wait, so 10 - inch pizza: cost per square inch (in dollars) is \(\frac{10}{78.5}\approx0.13\) (since \(10\div78.5\approx0.127\approx0.13\)), 16 - inch pizza: \(\frac{20}{200.96}\approx0.0995\approx0.1\) dollars per square inch. So the 10 - inch pizza costs about 0.13 dollars per square inch (or 13 cents), the 16 - inch costs about 0.1 dollars per square inch (or 10 cents). Wait, but the question says "The 10 - inch pizza costs about ___ ¢ per square inch. The 16 - inch pizza costs about ___ ¢ per square inch. The ___ pizza is a better deal." Wait, no, wait, if 16 - inch has lower cost per square inch, it's a better deal. Wait, my calculation was wrong. Let's redo:

For 10 - inch pizza:
- Diameter \(d = 10\) in, radius \(r=\frac{10}{2}=5\) in.
- Area \(A=\pi r^{2}=3.14\times5^{2}=3.14\times25 = 78.5\) in².
- Cost \(C = \$10=1000\) cents.
- Cost per square inch: \(\frac{1000}{78.5}\approx12.74\) cents \(\approx13\) cents (or \(0.13\) dollars per square inch).

For 16 - inch pizza:
- Diameter \(d = 16\) in, radius \(r=\frac{16}{2}=8\) in.
- Area \(A=\pi r^{2}=3.14\times8^{2}=3.14\times64 = 200.96\) in².
- Cost \(C=\$20 = 2000\) cents.
- Cost per square inch: \(\frac{2000}{200.96}\approx9.95\) cents \(\approx10\) cents (or \(0.1\) dollars per square inch).

Wait, but the options for the first blank (10 - inch cost per square inch) are 0.13, and for 16 - inch are 0.1? Wait, maybe the question is in dollars per square inch? Let's check the options: the numbers are 0.1, 0.13, 10 - inch, 16 - inch.

So:

1. Cost per square inch for 10 - inch: \(\frac{10}{78.5}\approx0.127\approx0.13\) dollars per square inch.

2. Cost per square inch for 16 - inch: \(\frac{20}{200.96}\approx0.0995\approx0.1\) dollars per square inch.

3. Since 0.1 (16 - inch) is less than 0.13 (10 - inch), the 16 - inch pizza is a better deal? Wait, no, wait, 0.1 dollars per square inch is less than 0.13, so 16 - inch is cheaper per square inch, so better deal.

Wait, but the options for the last blank are "10 - inch" and "16 - inch". So:

- The 10 - inch pizza costs about 0.13 ¢? No, 0.13 dollars is 13 cents. Wait, maybe the question has a typo, but let's go with the numbers.

So step by step:

Step1: Calculate area of 10 - inch pizza

\(A_{10}=\pi(\frac{10}{2})^{2}=25\pi\approx78.5\) in². Cost is \(\$10\). Cost per square inch: \(\frac{10}{78.5}\approx0.13\) dollars per square inch (or 13 cents per square inch).

Step2: Calculate area of 16 - inch pizza

\(A_{16}=\pi(\frac{16}{2})^{2}=64\pi\approx200.96\) in². Cost is \(\$20\). Cost per square inch: \(\frac{20}{200.96}\approx0.1\) dollars per square inch (or 10 cents per square inch).

Step3: Compare cost per square inch

0.1 (16 - inch) < 0.13 (10 - inch), so 16 - inch pizza is a better deal.

Answer:

The 10 - inch pizza costs about 0.13 ¢ per square inch? Wait, no, 0.13 dollars is 13 cents. Wait, the first blank (10 - inch cost per square inch) should be 0.13, the second (16 - inch) 0.1, and the third "16 - inch". So:

First blank: 0.13, Second blank: 0.1, Third blank: 16 - inch.