To find how much greater the area of the large pizza is compared to the small pizza, we need to calculate the area of both pizzas.
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Calculate the area of the small pizza:
- The diameter of the small pizza is 10 inches, so the radius \( r \) is: \[ r = \frac{10}{2} = 5 \text{ inches} \]
- The area \( A_s \) of a circle is given by the formula: \[ A = \pi r^2 \]
- Therefore, the area of the small pizza is: \[ A_s = \pi (5)^2 = \pi (25) = 25\pi \text{ square inches} \]
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Calculate the area of the large pizza:
- The diameter of the large pizza is 14 inches, so the radius \( r \) is: \[ r = \frac{14}{2} = 7 \text{ inches} \]
- Thus, the area \( A_l \) of the large pizza is: \[ A_l = \pi (7)^2 = \pi (49) = 49\pi \text{ square inches} \]
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Find the difference in area between the large pizza and the small pizza:
- The difference in area is: \[ A_l - A_s = 49\pi - 25\pi = (49 - 25)\pi = 24\pi \text{ square inches} \]
Thus, the area of the large pizza is \( 24\pi \) square inches greater than the area of the small pizza.
The correct answer is C. \(24\pi\) square inches.