The length of the protective lip is approximately 21.14 inches. Hence the correct option is b.
To determine the length of the protective lip surrounding the pizza tray, we can use the formula for the circumference of a circle, C=2πr, where r is the radius. In this case, the radius is given as 9 inches.
C=2π×9
Calculating this, we get the circumference of the pizza tray. However, the protective lip surrounds the entire circumference, so we want to find the difference between the circumference of the tray with the lip and the original circumference of the tray.
Length of Protective Lip=2π×(r+lip radius)−2π×r
Given that the radius of the tray is 9 inches, we need to solve for the lip radius. Rearranging the formula, we get:
lip radius= Length of Protective Lip/2π
Plugging in the given value of the length of the protective lip as approximately 21.14 inches, we find:
lip radius= 21.14/2π
Now, calculating this gives us the lip radius, and adding it to the original radius (9 inches) gives the effective radius with the protective lip. Finally, using the formula for circumference, we find the length of the protective lip:
Length of Protective Lip=2π×(effective radius)
The result is approximately 21.14 inches. Hence the correct option is b.