Question

Given that the cost of a 10 inch (in diameter) pizza is $11 and the cost of a 20 inch pizza (in diameter) is $22, would it make more sense to buy two 10 inch pizzas or one 20 inch pizza? Explain your answer in detail.

Answer 1

it makes more sense to buy one 20 inch pizza

Explanation:

step 1

Find the area of a 10 inch pizza

The area of a pizza ( circle) is equal to

`A=\pi r^(2)`

we have

`r=10/2=5\ in` ---> the radius is half the diameter

substitute

`A=\pi (5)^(2)`

`A=25\pi\ in^2`

assume

`\pi =3.14`

`A=25(3.14)=78.5\ in^2`

step 2

Find the cost of a 10 in pizza per square inch

Divide the cost by the area

`(11)/(78.5)= \$0.14\ per\ square\ inch`

step 3

Find the area of a 20 inch pizza

The area of a pizza ( circle) is equal to

`A=\pi r^(2)`

we have

`r=20/2=10\ in` ---> the radius is half the diameter

substitute

`A=\pi (10)^(2)\\A=100\pi\ in^2`

assume

`\pi =3.14`

`A=100(3.14)=314\ in^2`

step 4

Find the cost of a 20 in pizza per square inch

Divide the cost by the area

`(22)/(314)= \$0.07\ per\ square\ inch`

therefore

it makes more sense to buy one 20 inch pizza (because the unit rate is less)