# A rectangular pizza, 40 cm by 60 cm, is cut into 24 square pieces. Two round pizzas, each cut into 12 slices, also give 24 pieces. So that the pizzas are the same size, what must be the diameter of the round pizzas?

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## 40*60 = 2400 sq. cm

A = pi * r^2
2400 = 3.14 * r^2
764.33 = r^2
_____ = diameter

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## the area of the round pizzas is equal to the rectangular pizza

2 π r^2 = 40 * 60 ... r^2 = 1200 / π

diameter = 2 r

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## To find the diameter of the round pizzas, we need to calculate the area of both the rectangular pizza and the round pizzas.

Step 1: Calculate the area of the rectangular pizza.
The area of a rectangle is given by the formula: A = length x width.
In this case, the length of the rectangular pizza is 60 cm and the width is 40 cm.
So, the area of the rectangular pizza is A_rectangle = 60 cm x 40 cm = 2400 cm^2.

Step 2: Calculate the area of one square piece from the rectangular pizza.
Since the rectangular pizza is cut into 24 square pieces, the area of one square piece will be the total area of the rectangular pizza divided by the number of pieces. Therefore, A_square = A_rectangle / 24 = 2400 cm^2 / 24 = 100 cm^2.

Step 3: Calculate the area of one round pizza slice.
The round pizzas are also cut into 24 pieces. Since 24 is evenly divisible by 12, each round pizza is cut into 12 slices of equal size.
Therefore, the area of one round pizza slice will be twice the area of one square piece from the rectangular pizza.
So, A_round_slice = 2 x A_square = 2 x 100 cm^2 = 200 cm^2.

Step 4: Calculate the diameter of the round pizzas.
The area of a circle is given by the formula: A = πr^2, where r is the radius of the circle.
Since we know the area of one round pizza slice and want to find the diameter, we can use the formula: A = π(d^2)/4, where d is the diameter of the circle.
Therefore, 200 cm^2 = π(d^2)/ 4.

Step 5: Rearrange the equation to solve for d.
Multiplying both sides of the equation by 4 gives us: 800 cm^2 = π(d^2).
Dividing both sides of the equation by π gives us: 800 cm^2 / (π) = d^2.
Finally, taking the square root of both sides gives us: √(800 cm^2 / (π)) = d.
Using a calculator, we find that d ≈ 16.02 cm.

Therefore, the diameter of the round pizzas must be approximately 16.02 cm to make the pizzas the same size as the rectangular pizza.

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## To find the diameter of the round pizzas, we need to determine the area of both the rectangular pizza and the round pizza.

The area of the rectangular pizza can be calculated by multiplying its length by its width: Area_rectangular = Length × Width = 40 cm × 60 cm = 2400 cm².

Since the rectangular pizza is divided into 24 square pieces, we can find the area of each square piece by dividing the total area of the rectangular pizza by the number of pieces: Area_each_square = Area_rectangular / Number_of_pieces = 2400 cm² / 24 = 100 cm².

Now, let's consider the round pizzas. The area of a circle can be calculated using the formula: Area_circle = π × (Radius)².

Since the round pizzas are divided into 24 slices, each slice will have an area equal to: Area_each_slice = Area_circle / Number_of_slices.

Since the area of each slice is equal to the area of each square piece, we can equate the two formulas and solve for the radius (which will be half the diameter) of the round pizzas.

So, we have: 100 cm² = (π × (Radius)²) / 12.

To solve for the radius, we rearrange the equation: (π × (Radius)²) = 12 × 100 cm².

Dividing both sides by π gives us: (Radius)² = (12 × 100 cm²) / π.

And finally, taking the square root of both sides will give us the radius of the round pizzas: Radius = √((12 × 100 cm²) / π).

To get the diameter, we multiply the radius by 2: Diameter = 2 × Radius.

Calculating this using a numerical value for π (approximately 3.14), we can find the diameter of the round pizzas in centimeters.