Final answer:
The largest circle that can fit inside a square with a side of 16 cm has a radius of 8 cm. Using the area formula A = πr², the area of the circle is calculated to be 201.0619298 cm², which we round to 200 cm² to match the precision of two significant figures given for the circle's radius.
Step-by-step explanation:
Finding the Area of the Largest Circle in a Square
To find the area of the largest circle that can fit in a square with a side of 16 cm, we consider the diameter of the circle, which is equal to the side length of the square. Since the diameter is twice the radius (d = 2r), we divide the side length by 2 to obtain the radius of the circle. Hence, the radius (r) is 8 cm.
Now, we calculate the circle's area using the formula for the area of a circle, A = πr². For our specific case:
A = π × (8 cm)²
A = π × 64 cm²
A = 3.1415927… × 64 cm²
A = 201.0619298 cm²
Since our radius was given to a precision of two significant figures (8 cm), we should express the area to two significant figures as well:
A = 200 cm² (rounded to two significant figures)