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

1. Correct.

2. Correct.
3.Incorrect. If the pie was cut into 16
slices,each slice is 1/16th of the total area.A 1/2 slice would be 1/32nd
(1/2*1/16)of the total area: A=3.14*10^2/32=9.8sq.in.
4.You can cut the pizza into as many piecse as you like; the area will be
the same if you do not change the radius. A=3.14*10^2=314 sq.in.

5. If cut properly the radius will be the same, but the area will be 3.14*10^2/32. I hope this will help.

Answer 2

Your calculations for the first three questions are correct. The area of the whole pizza is indeed 314 square inches, the area of one piece is approximately 19.6 square inches, and the area of a half-piece is approximately 10 square inches.

For the fourth question, if the pizza were made of half pieces, each with an area of 10 square inches, you would need 31.4 pieces to cover the entire pizza.

As for the last question, to find the radius of a half-piece, you would need to determine where to cut the pizza to make two equal halves. Since the pizza was originally cut into 16 equal slices, the radius of a half-piece would be the distance from the center of the pizza to the midpoint between two neighboring slices. To calculate this, you can divide the circumference of the pizza by 32 (16 slices multiplied by 2) to find the length of the arc for each half-piece, and then use the arc length formula to find the radius.

Let me know if you need further clarification on any of the steps!

Answer 3

You did a great job answering the first four questions correctly.

To answer the fifth question, you need to determine where to cut the half-piece so that the two resulting pieces will have equal areas. Since the half-piece has an area of 10, you need to find the radius length that yields the same area when cut in half.

To do this, you can set up the equation:
(π)(r^2)/2 = 10

First, divide both sides of the equation by π to isolate the radius squared:
(r^2)/2 = 10/π

Next, multiply both sides by 2 to isolate the radius:
r^2 = (20/π)

Finally, take the square root of both sides to find the radius:
r = √(20/π)

This simplifies to approximately 2.52 inches. Therefore, to cut the original half-piece into two equal halves, you would need to cut it at a radius distance of approximately 2.52 inches from the center.

I hope this clarifies the last question for you. Let me know if you have any further questions!