To find the area of the red part of the target, subtract the areas of the inner circles from the total area of the target. Use the equation A = Area - 4 × Area of inner circle to find the area of the red part, knowing that the total area is 2826 cm².
Step-by-step explanation:
To find the area of the red part of the target, we need to subtract the areas of the inner circles from the total area of the target. The radius of the target is given as 30.0 cm, so the area of the entire target is:
Area = πr² = 3.14 × (30.0 cm)² = 2826 cm²
Next, we need to find the area of the inner circles. Since all the bands are the same width, the radius of the inner circles will be 30.0 cm minus the width of one band. Let's assume the width of one band is x cm. The area of each inner circle will be:
Area of inner circle = π(30.0 cm - x)²
Let's say the area of the red part is A cm². We can set up an equation:
A = Area - 4 × Area of inner circle
Since the area of the red part is given as 1766.3 cm², we can solve the equation to find the value of x:
1766.3 = 2826 - 4 × π(30.0 - x)²
Solving this equation will give us the value of x, which is the width of one band. With that value, we can find the area of the red part.
The probable question can be: 15. Carla drew a target on the floor for a bean bag game. The radius of the target is 30.0 cm, and all bands are the same width. What area of the target is red?