Question

A mexican restaurant sells quesadillas in two sizes: a “large” 12 inch-round quesadilla and a “small” 6 inch-round quesadilla. Which is larger, half of the 12-inch quesadilla or the entire 6 inch quesadilla?

Answer 1

"half of the 12-inch quesadilla" is larger

Explanation:

The "inch size" is the diameter of the circular quesadilla.

The area of circle is given by
`\pi r^2`

We also know radius is half of diameter.

HALF OF 12-INCH QUESADILLA:

12in diameter = 6 inch radius, the area is:

`\pi(6)^2=36\pi`

Half of this is:

`(36\pi)/(2)=18\pi`

ENTIRE 6-INCH QUESADILLA:

6 inch diameter means 6/2 = 3 inch radius

The area of this is:

`\pi(3)^2 = 9\pi`

So, we can say that "half of the 12-inch quesadilla" is larger.