The box is a square. its perimeter is 48 inches. the pizza has a circumference of 37.68 inches. what is the difference in the area of the pizza and the area of the pizza box? round to the nearest hundredth ( 2 decimal places).

The difference between the area of the pizza and the area of the pizza box is 10.32 inches.

We need to find the dimension of the square and circle before finding the area of each object.

Find the dimension of the square (the side)
The perimeter of the square is 48 in, the perimeter is the sum of four congruent sides.
p = 48
4s = 48
s = 48/4
s = 12
The side of the square is 12 in

Find the dimension of the circle (the radius)
The circumference of the circle is 37.68 in
c = 37.68
2πr = 37.68
πr = 37.68/2
πr = 18.84
r = 18.84/π
r = 18.84/3.14
r = 6
The radius of the circle is 6 in

Find the area of the square and the circle
a square = s²
a square = 12²
a square = 144
The area of the square is 144 in²

a circle = πr²
a circle = π(6²)
a circle = π(36)
a circle = 3.14(36)
a circle = 113.04
The area of the circle is 113.04 in²

Find the difference between area of square and area of circle
difference = a square - a circle
difference = 144 - 113.04
difference = 30.96

The difference of the area is 30.96 in²

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