Video Transcript
The bull’s eye on the given archery
target has a radius of three inches. The entire target has a radius of
15 inches. Determine the area of the target
outside of the bull’s eye, rounded to the nearest square inch.
The bull’s eye is the very center
of the target; that’s the circle colored orange. We’re told that the bull’s eye has
a radius of three inches and that the entire target has a radius of 15 inches. Remember, the radius of any circle
is the distance from its center to its edge.
We want to determine the area of
the target that is outside of the bull’s eye, which will be the difference between
the area of the entire target and the area of the bull’s eye itself. As each of these are circles, we
need to recall that the area of a circle is equal to 𝜋 multiplied by its radius
squared. We can substitute the radius of
each circle into this formula.
The target has an area of 𝜋
multiplied by 15 squared, and the bull’s eye has an area equal to 𝜋 multiplied by
three squared. Evaluating each of the squares
gives 225𝜋 minus nine 𝜋. And then, subtracting gives
216𝜋.
We’re asked to give the answer to
the nearest square inch. So evaluating this as a decimal
first gives 678.584 continuing. And then, we round to the nearest
integer.
By subtracting the area of the
bull’s eye from the total area of the target, we’ve found that the area outside the
bull’s eye, to the nearest square inch, is 679 square inches.
