In a party , there are three different sizes of pizzas of radius 7 inches , 9 inches and 12 inches . 7 inches pizzas is sliced in 7 slices, 9 inches pizza is sliced in 9 slices and 12 inches pizza is sliced in 12 slices . If you have option to choose only one slice, which pizza slice is the largest ?

Options

A. 7 inches pizza
B. 9 inches pizza
C. 12 inches pizza
D. All are same

Answer

To determine which pizza slice is the largest, we need to calculate the area of each slice from the three different sizes of pizzas.

### Step-by-Step Solution:

1. **Calculate the area of the 7-inch pizza:**
- The formula for the area of a circle is \( A = \pi r^2 \).
- For the 7-inch pizza, the radius \( r = 7 \) inches.
- Area = \( \pi \times 7^2 = \pi \times 49 = 49\pi \) square inches.
- Since this pizza is sliced into 7 slices, the area of one slice is:
\[ \text{Area of one slice} = \frac{49\pi}{7} = 7\pi \text{ square inches.} \]

2. **Calculate the area of the 9-inch pizza:**
- For the 9-inch pizza, the radius \( r = 9 \) inches.
- Area = \( \pi \times 9^2 = \pi \times 81 = 81\pi \) square inches.
- Since this pizza is sliced into 9 slices, the area of one slice is:
\[ \text{Area of one slice} = \frac{81\pi}{9} = 9\pi \text{ square inches.} \]

3. **Calculate the area of the 12-inch pizza:**
- For the 12-inch pizza, the radius \( r = 12 \) inches.
- Area = \( \pi \times 12^2 = \pi \times 144 = 144\pi \) square inches.
- Since this pizza is sliced into 12 slices, the area of one slice is:
\[ \text{Area of one slice} = \frac{144\pi}{12} = 12\pi \text{ square inches.} \]

4. **Compare the areas of the slices:**
- Area of one slice of 7-inch pizza = \( 7\pi \) square inches.
- Area of one slice of 9-inch pizza = \( 9\pi \) square inches.
- Area of one slice of 12-inch pizza = \( 12\pi \) square inches.

5. **Determine the largest slice:**
- Comparing \( 7\pi \), \( 9\pi \), and \( 12\pi \), it is clear that \( 12\pi \) is the largest.

### Conclusion:
The largest pizza slice is from the 12-inch pizza, with an area of \( 12\pi \) square inches.

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