Final answer:
The area of a circle with an 18 cm radius is calculated using the formula A = πr², which results in an exact area of 324π cm². The area expressed with two significant figures is 320π cm².
Step-by-step explanation:
The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius of the circle. If the radius is 18 cm, we plug it into the formula: A = π(18 cm)².
Calculating this, A = π(324 cm²) = 3.14159... × 324 cm².
Since π is a number that cannot be precisely defined, we can give the exact answer in terms of π: the area A = 324π cm².
When significant figures are taken into account, if only two significant figures are present in the measurement (for example, if the radius were given as 18 cm with only two significant figures), the final answer would also be reported with two significant figures. In this case, it would be appropriately expressed as 3.2×10²π cm² or approximately 320π cm².