I have a pizza. The radius is 10 inches long. The pizza was cut into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.

Question

I have a pizza. The radius is 10 inches long. The pizza was cut into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.

1. Find the area of the whole pizza.
a=(pi)(10^2), =314

2. What is the area of one piece of pizza?
(pi)(r^2)/16, 100(pi)/16=19.6

3. What is the area of a half-piece?
100(pi)/36=10
4. What would the area of the whole pizza be if it were made of half pieces?
a=10(pi), a=100/10, a=10
5. What is the radius of a half-piece? (ie, where do I need to cut to make two equal halves out of a piece?)

I was wondering if I got these answers correct. If I did not, could someone please explain what I did wrong?Also, I was a little confused as to how to get the answer to the last question. Cheers!

Answer 1

Your answers to the first three questions are correct. Let's go through the rest of the questions to verify your answers.

4. To find the area of the whole pizza if it were made of half pieces, we need to consider that the original pizza has 16 equal slices, and when one slice was left, it was cut into two unequal halves.

Since the original pizza had 16 slices, and each slice had an area of approximately 19.6 square inches (as you calculated in question 2), the total area of the original pizza would be 16 times that, which is 19.6 * 16 = 313.6 square inches. So, the correct answer is approximately 313.6 square inches, not 10.

5. To determine where to cut the slice into two equal halves, imagine a line dividing the half-slice vertically from top to bottom. This line should pass through the center of the pizza (because the original pizza was perfectly symmetrical). This means the distance from the center to the edge of the half-slice would be the desired radius of a half-piece.

So, in this case, the radius of a half-piece would be half of the original radius, which is 10/2 = 5 inches. The correct answer is 5 inches.

So, to summarize:
1. The area of the whole pizza is approximately 314 square inches.
2. The area of one piece of pizza is approximately 19.6 square inches.
3. The area of a half-piece is approximately 10 square inches.
4. The corrected area of the whole pizza if it were made of half pieces is approximately 313.6 square inches.
5. The radius of a half-piece is 5 inches.

Your calculations were mostly correct, but there was a mistake in question 4. Take note of the correction provided.