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27-04-2020
Mathematics

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A circular pizza with a 16-inch diameter is cut into 8 equal slices. A square pizza is cut into 9 equal-size pieces. To the nearest inch, find the dimensions of the square pizza so that each of its 9 pieces has the same area as one slice of the round pizza. Remember: Circumference= ⋅Diameter, Area= 2 r2 (r is radius). Talk to your teacher or a friend if you need to talk about the problem. The dimensions are . I know this because ___. Optional Extension: If a box is made to exactly fit the square pizza, will the circular pizza fit into the box?

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dribeiro dribeiro

03-05-2020

Answer:

The square pizza should be 15.03 x 15.03.

The circular pizza wont fit in a box made for the square pizza, since the diameter of the circular pizza is greater than the side of the square pizza.

Step-by-step explanation:

In order to solve this problem we first need to calculate the area of the circular pizza, it's given by the following formula:

area = pi*(d/2)² = 3.14*(16/2)² = 200.96 square inches

Each slice has the following area:

slice = area/8 = 200.96/8 = 25.12 square inches

The area of a square pizza is given by:

area = width²

This is to be divided in 9 squares, so:

slice = area/9 =( width²)/9

25.12 = (width²)/9

width² = 25.12*9 = 226.08

width = sqrt(226.08) = 15.03 inches

The square pizza should be 15.03 x 15.03.

The circular pizza wont fit in a box made for the square pizza, since the diameter of the circular pizza is greater than the side of the square pizza.

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