Final answer:
To find the amount of felt left over, the area of the square (64 cm²) is calculated, then the area of the circle (28.27 cm², rounded to two significant figures) is subtracted, leaving 35.73 cm² (rounded to 36 cm² with two significant figures) of felt remaining.
Step-by-step explanation:
The amount of felt left over after cutting a circle with a radius of 3 centimeters from a square piece of felt with sides 8 centimeters long can be found by calculating the area of the square and then subtracting the area of the circle.
First, find the area of the square by squaring the side length:
- Area of square = side × side = 8 cm × 8 cm = 64 cm².
Next, calculate the area of the circle using the formula A = πr²:
- Area of circle = π × (3 cm)² = 28.27 cm² (rounded to two significant figures since the radius has two significant figures).
Finally, subtract the area of the circle from the area of the square to find the area of felt remaining:
- Felt remaining = Area of square - Area of circle = 64 cm² - 28.27 cm² = 35.73 cm².
Note that here the areas are given to two decimal places to provide an exact answer, but in practice, you might report it with the same number of significant figures as the inputs, which is two, resulting in 36 cm² of felt remaining.