Final answer:
To determine the upper and lower bounds of the radius and circumference of a circle when the area is given to two significant figures, use the area formula A = πr² to find the bounds of the radius, and then apply C = 2πr to calculate the bounds of the circumference.
Step-by-step explanation:
The area of a circle is given to 2 significant figures (s.f.), which suggests the area is known to a certain precision. If the area (A) is 4.5 m² to two significant figures, we need to find the upper and lower bounds of the radius (r) and the circumference (C) of the circle.
First, use the formula for the area of a circle, which is A = πr². To find the bounds of the radius, consider the smallest area that would round up to 4.5 m² (e.g., 4.45 m²) and the largest area that would round down to 4.5 m² (e.g., 4.55 m²). Solve for r using these bounds:
- Lower bound for r: A = πr² = 4.45 m²
- Upper bound for r: A = πr² = 4.55 m²
Now, calculate the corresponding circumference using C = 2πr, with the lower and upper bounds of r.