Question

Pete's Pizzeria offers two sizes of pizza, as shown below.

The small pizza is a circle with a diameter of 10 inches. The large pizza is a circle with a diameter of 14 inches.

How much greater is the area of the large pizza compared to the small pizza?

A.
4
π
square inches

B.
16
π
square inches

C.
24
π
square inches

D.
96
π
square inches

Answer 1

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.

1. **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:
\[
A_s = \pi (5)^2 = \pi (25) = 25\pi \text{ square inches}
\]

2. **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:
\[
A_l = \pi (7)^2 = \pi (49) = 49\pi \text{ square inches}
\]

3. **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**.