Question

The center on a target has a diameter of 3 inches. The whole target has a diameter of 15 inches. Complete the explanation for what part of the whole target is the center. The center of the target takes up _________% of the whole target.

Answer 1

So the center takes up 4% of the whole target.

Explanation:

Since both the center and the target are circles and we want to compare then we first need to find their area. The area of a circle is given by the formula bellow:

area = π*r²

Where r is the radius that is half the diameter.

For the whole target we have:

area_target = π*(15/2)² = π*(7.5)² = π*56.25 square inches

For the center:

area_center = π*(3/2)² = π*(1.5)² = π*2.25 square inches

In this case since we want to compare the areas we won't multiply the value of π since that would increase the error of our results. Now that we have both areas we need to calculate how many percents does the center takes from the whole target. For that we can use a rule of three, such as:

π*56.25 -> 100%

π*2.25 -> x %

(π*56.25)/(π*2.25) = 100/x

(56.25)/(2.25) = 100/x

56.25*x = 100*2.25

x = 225/56.25 = 4

So the center takes up 4% of the whole target.