To find out how the area of an extra large pizza compares to a small pizza when the diameter of the extra large pizza is twice that of the small pizza, we can use the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
Let’s denote the diameter of the small pizza as \(d\). Therefore, the radius \(r\) of the small pizza is:
\[ r_{\text{small}} = \frac{d}{2} \]
The area of the small pizza is:
\[ \text{Area}_{\text{small}} = \pi \left( \frac{d}{2} \right)^2 = \pi \frac{d^2}{4} \]
Now, the diameter of the extra large pizza is twice that of the small pizza, which means:
\[ d_{\text{extra large}} = 2d \]
Thus, the radius of the extra large pizza is:
\[ r_{\text{extra large}} = \frac{2d}{2} = d \]
The area of the extra large pizza is:
\[ \text{Area}_{\text{extra large}} = \pi d^2 \]
Now, we can compare the areas:
\[ \frac{\text{Area}{\text{extra large}}}{\text{Area}{\text{small}}} = \frac{\pi d^2}{\pi \frac{d^2}{4}} = \frac{d^2}{\frac{d^2}{4}} = 4 \]
So, the area of the extra large pizza is 4 times the area of the small pizza.
The correct answer is:
C. extra large is 4 times the area of a small.