SOLUTION: 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 l

Question 318758: 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?)
x=7.158
6. How far up the radius from the center of the circle will I need to cut so we will both have an equal area of pizza?

And Jenny and Greg have both agreed to mow half of a lawn. This lawn is a rectangle, 25 feet by 45 feet. Their lawn mower cuts a 2 feet wide path. If Jenn starts at a corner and makes a path around the outside, how many times should she go around to cut one half of the lawn?
2
My answers were incorrect. Could someone please explain how to get the correct answers? Cheers!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1. Correct.
2. Correct.
3. Incorrect, I'm assuming a half-piece is one slice cut in half?

4. You mean 16 half-pieces or 32 half-pieces?

5. What is the radius of a circle where the area is (1/2) the original area.

inches
6. I'm not sure I understand the question. If you make a circumferential cut of the pizza at R=7.07, you will cut the area of the pizza in half.
.
.
.
The rectangle's area is,

She needs to mow until there is 562.5 sq. ft. left.
Each cut takes (2+2=)4 feet off the width and 4 feet off the length of the rectangle to be mowed.
On her first cut, the area left to be mowed is reduced to,

On her second cut, the area left to be mowed is reduced to,

She then needs to cut another (629-562.5) sq.ft. or 66.5 sq.ft.
Since the mower is 2 ft. wide, she needs to move the mower another 66.5/2=33.25 ft off of the remaining 37x17 foot rectangle.
So 2 times around plus 33.25 feet would be exactly half.
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