Final answer:
To determine if the personal-size pizza will fit on a plate with a radius of 10√ inches or a radius of 12√ inches, we need to compare the sizes of the pizza and the plate. We can use the formula for the area of a circle to calculate the areas and determine if the pizza will fit. The approximate values of the radii are 10√ ≈ 3.16 inches and 12√ ≈ 4.47 inches.
Step-by-step explanation:
To determine if the personal-size pizza will fit on a plate with a radius of 10√ inches or a radius of 12√ inches, we need to compare the size of the pizza to the size of the plate. The area of the pizza can be found using the formula A = πr², where r is the radius of the pizza. The area of the plate can also be found using the same formula, but with the radius of the plate. If the area of the pizza is smaller than the area of the plate, then the pizza will fit on the plate. If the area of the pizza is larger, then it won't fit.
First, let's calculate the approximate values of each radius. The given radii are 10√ and 12√. To find their approximate values, we can multiply the square root of 10 and 12 by the square root of 10, which is approximately 3.16 inches, and the square root of 12, which is approximately 4.47 inches, respectively.
So, based on the approximate values of each radius, we can conclude that the pizza will fit on a plate with a radius of 10√ inches (approximately 3.16 inches). Therefore, the correct answer is option C) No, it won't fit; 10√ ≈ 3.16 inches.