The area of the rectangular sheet of cardboard is:
100 cm x 60 cm = 6000 cm²
The diameter of each badge is 14 cm, so the radius is 7 cm. The formula for the area of a circle is:
A = πr²
Using 3.14 as pi, we get:
A = 3.14 x 7² = 153.86 cm²
To find how many badges can be cut out of the sheet, we divide the area of the sheet by the area of each badge:
6000 cm² / 153.86 cm² ≈ 38.99649032
Since Alex can only cut whole badges, he can cut out 38 badges.
The area of the cardboard used for the badges is:
38 x 153.86 cm² = 5848.68 cm²
To find the area of the cardboard left over, we subtract the area used for the badges from the total area:
6000 cm² - 5848.68 cm² = 151.32 cm²
Therefore, the area of the cardboard left over is 151.32 cm².