Final answer:
The upper and lower bounds for the circumference and area of a circle with a radius of 4.00 cm to 2 d.p. are calculated using the formulas C = 2πr and A = πr², accounting for the slight possible variation in the actual radius measure.
Step-by-step explanation:
The given radius of a circle is 4.00 cm to 2 decimal places (d.p.), which means the possible radius lies between 3.995 cm and 4.005 cm (exclusive).
This range is because the next incremental value at the third decimal place could either be a 5 if we round up or stay as a 4 if we round down.
We can use this to calculate the upper and lower bounds of both the circumference and area of a circle using the specified radius.
a) Circumference: We know that the circumference (C) of a circle can be calculated using the formula C = 2πr. Therefore, the lower bound for the circumference is 2π(3.995) and the upper bound is 2π(4.005).
b) Area: Similarly, the area (A) of a circle can be calculated with the formula A = πr².
Thus, the lower bound for the area is π(3.995)² and the upper bound is π(4.005)².