Questions: 11) If a 12 inch diameter pizza requires 10 ounces of dough, how much dough is needed for a 16 inch pizza? Assume that both pizzas are 1 inch thick.

11) If a 12 inch diameter pizza requires 10 ounces of dough, how much dough is needed for a 16 inch pizza? Assume that both pizzas are 1 inch thick.
Transcript text: 11) If a 12 inch diameter pizza requires 10 ounces of dough, how much dough is needed for a 16 inch pizza? Assume that both pizzas are 1 inch thick.
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Solution

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Solution Steps

Step 1: Find the radius of each pizza.

The radius is half the diameter. Radius of the 12-inch pizza: 12/2 = 6 inches Radius of the 16-inch pizza: 16/2 = 8 inches

Step 2: Find the area of each pizza.

The area of a circle is given by \(A = \pi r^2 \). Area of the 12-inch pizza: \(\pi (6^2) = 36\pi\) square inches. Area of the 16-inch pizza: \(\pi (8^2) = 64\pi\) square inches.

Step 3: Set up a proportion and solve for x.

We can set up a proportion relating the area of each pizza to the amount of dough needed. \(\frac{36\pi}{10} = \frac{64\pi}{x}\) Cross-multiply: \(36\pi x = 640\pi\) Divide both sides by \(36\pi\): \(x = \frac{640\pi}{36\pi} = \frac{640}{36} = \frac{160}{9}\)

Final Answer

\\(\boxed{x = \frac{160}{9} \approx 17.78 \text{ ounces}}\\)

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