Question

A Mexican restaurant sells quesadillas in two sizes: a "large" 10 inch-round quesadilla and a "small" 5 inch-
round quesadilla. Which is larger, half of the 10-inch quesadilla or the entire 5-inch quesadilla?

Answer 1

Answer:

Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^2$

where

r is the radius

step 1

Find the area of the 10 inch-round quesadilla

we have

$D=10\ in$

$r=10/2=5\ in$

substitute

$A=\pi (5)^2$

$A=25\pi\ in^2$

step 2

Find the area of the 5 inch-round quesadilla

we have

$D=5\ in$

$r=5/2=2.5\ in$

substitute

$A=\pi (2.5)^2$

$A=6.25\pi\ in^2$

step 3

Which is larger, half of the 10-inch quesadilla or the entire 5-inch quesadilla?

Compare

half of the 10-inch quesadilla is equal to ----> $\frac{1}{2}(25\pi)=12.5\pi\ in^2$

the entire 5-inch quesadilla ---->$6.25\pi\ in^2$

therefore

Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla