If a $$ 12^{\prime \prime} $$ pepperoni pizza from a pizza parlor costs $$ \$ 9.43 $$, what should a $$ 16^{\prime \prime} $$ pizza from the pizza parior cost? The $$ 16^{\prime \prime} $$ pizza should cost $$ \$ \square $$. (Round to the nearest cent as needed.)

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UpStudy AI · Accepted Answer

Let the cost be proportional to the area of the pizza.

1. The area $$ A $$ of a circle with diameter $$ d $$ is given by:
   $$
   A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4}
   $$

2. For a $$12^{\prime\prime}$$ pizza, the area is:
   $$
   A_{12} = \frac{\pi (12)^2}{4} = \frac{\pi \cdot 144}{4} = 36\pi
   $$
   and the cost is $$\$9.43$$.

3. For a $$16^{\prime\prime}$$ pizza, the area is:
   $$
   A_{16} = \frac{\pi (16)^2}{4} = \frac{\pi \cdot 256}{4} = 64\pi
   $$

4. The cost per unit area based on the $$12^{\prime\prime}$$ pizza is:
   $$
   \text{Cost per unit area} = \frac{9.43}{36\pi}
   $$

5. Then, the cost of the $$16^{\prime\prime}$$ pizza is:
   $$
   \text{Cost} = \frac{9.43}{36\pi} \times 64\pi = 9.43 \times \frac{64}{36}
   $$
   Simplify the fraction:
   $$
   \frac{64}{36} \approx 1.7778
   $$

6. Multiply to find the cost:
   $$
   9.43 \times 1.7778 \approx 16.76
   $$

Thus, the $$16^{\prime\prime}$$ pizza should cost $$ \$16.76 $$.
The $$16^{\prime\prime}$$ pizza should cost \$16.76.

If a pepperoni pizza from a pizza parlor costs , what should a pizza from the
pizza parior cost?
The pizza should cost .
(Round to the nearest cent as needed.)

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If a pepperoni pizza from a pizza parlor costs , what should a pizza from the pizza parior cost? The pizza should cost . (Round to the nearest cent as needed.)