Question

Poppy's Pizza is buying square boxes to put their pizzas in. The large box has an area of 196 square inches. What is the area of the largest possible pizza that could be placed into the box?

Answer 1

154 square inches

Explanation:

Watch the attached figure of the square pizza box and the largest pizza that can fit into it.

Let the each side of the square pizza box be a inches.

Radius of the largest pizza that can fit into it = Half of the side of the pizza box =
`(a)/(2)`

So, area of the square box = Side * Side

= a * a

= a² square inches

It has also been given that the large box has an area of 196 square inches.

So,

Area of the box = a²

=> 196 = a²

Flipping the sides of the equation, we get

=> a² = 196

Taking square root on both the sides,

√a² = √196

a = 14 inches

So,

Side of square box = 14 inches

Radius of the largest pizza that can fit into it =
`(a)/(2)`

=
`(14)/(2)`

= 7 inches

Area of the largest possible pizza that could be placed into the box

= π *radius² [since pizza is circular in shape]

=
`(22)/(7)` * 7²

=
`(22)/(7)` * 7 * 7

Cancelling out a pair of 7's from the top and bottom, we have

= 22 * 7

= 154 square inches