Question

The diagram shows a square pizza box with side lengths of 10 inches. In the box is a circular pizza with a radius of 5 inches. What is the difference between the area of box and the pizza? Use = 3.14 and round your answer to the nearest hundredth​

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Answer 1

Answer:

${ \rm{area \: of \: box = 10 \times 10}} \\ { \underline{ \rm{ \: \: = 100 \: in {}^{2} \: \: }}}$

and:

${ \rm{area \: of \: circle = \pi {r}^{2} }} \\ { \rm{ = 3.14 \times {(5)}^{2} }} \\ = { \underline{ \rm{ \: \: 78.5 \: in {}^{2} \: \: }}}$

Difference:

${ \rm{ = 100 - 78.5}} \\ \\ = { \boxed{ \rm{ \: 21.5 \: {in}^{2} \: }}}$

Answer 2

The difference between the area of the box and the pizza is 21.5 in².

What is the area?

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the two-dimensional surface of a three-dimensional object, the surface area is its counterpart.

$\text{Area of Square} = (\rm Side)^2$

$\text{Area of Circle} = \pi(\rm r)^2$

The difference between the area of the box and the pizza can be found by finding the difference between the area of the box and the area of the circle.

Now, the area of the square box with a side of 10 inches, can be written as,

$\text{Area of the Box} = \text{Area of the Square}$

                          $= a^2\\\\=(10)^2\\\\=100\rm\ in^2$

Thus, the area of the square box is 100 in².

The area of the pizza with a radius of 5 inches can be written as,

$\text{Area of the Pizza} = \text{Area of the circle}$

                            $= \pi r^2\\\\=\pi (5)^2\\\\=78.5\rm\ in^2$

Thus, the area of the pizza is 78.5 in².

Further, the difference between the area of the box and the pizza can be written as,

The difference between the area = Area of the box - Area of Pizza

                                                        = 100 in² - 78.5 in²

                                                         = 21.5 in²

Hence, the difference between the area of the box and the pizza is 21.5 in².

Learn more about the Area:

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