The bulls-eye on a target has a diameter of 3 inches. The whole target has a diameter of 15 inches. What part of the whole target is the bulls-eye? Explain.
THANK YOU!!
area of bulls-eye = π(1.5)^2 = 2.25π
area of whole target = π(7.5)^2 = 56.25π
so the bull's-eye is
2.25π/56.25π = 1/25
which reflects the property that the areas of different circles are proportional to the square of their corresponding diameters
ratio of diameters = 3 : 15 = 1 : 5
so ratio of areas = 1^2 : 5^2 = 1 : 25
What percent would that be?
The percent would be 0.04%, or 4% because 1/25, in percent form, is 4%.
3/15 = 1/5
To find out what part of the whole target is the bullseye, we need to compare the sizes of the bullseye and the whole target.
The bullseye has a diameter of 3 inches, while the whole target has a diameter of 15 inches.
To calculate the part of the whole target that the bullseye represents, we can use the formula for finding the area of a circle.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius of the circle.
Since the diameter is given, we can find the radius of each circle by dividing the diameter by 2.
For the bullseye:
Radius = diameter ÷ 2 = 3 inches ÷ 2 = 1.5 inches
For the whole target:
Radius = diameter ÷ 2 = 15 inches ÷ 2 = 7.5 inches
Now, we can find the areas of both circles:
Area of bullseye = π(1.5 inches)^2
Area of whole target = π(7.5 inches)^2
Dividing the area of the bullseye by the area of the whole target will give us the desired ratio:
Bullseye ratio = (Area of bullseye ÷ Area of whole target) × 100
Now we can calculate the ratio:
Bullseye ratio = (π(1.5 inches)^2 ÷ π(7.5 inches)^2) × 100
The π (pi) cancels out, so we're left with:
Bullseye ratio = (1.5 inches)^2 ÷ (7.5 inches)^2 × 100
Simplifying this expression, we get:
Bullseye ratio = (2.25 inches^2) ÷ (56.25 inches^2) × 100
Reducing the fraction, we have:
Bullseye ratio = 0.04 × 100
The bullseye ratio is thus 4%.
Therefore, the bullseye represents 4% of the whole target.