Final answer:
The area of a circle with a diameter of 14 units is calculated using the formula A = πr². Once we determine the radius to be 7 units, the area is calculated to be 153.86 units², which is 154 units² rounded to two significant figures.
Step-by-step explanation:
The question asks for the area of a circle with a diameter of 14 units. To find the area of a circle, we use the formula A = πr², where A is the area, π is a constant approximately equal to 3.14, and r is the radius of the circle. Since the diameter is twice the radius, we first need to determine the radius, which would be half of the diameter, giving us a radius of 7 units.
Using the radius, we calculate the area as follows:
- A = πr²
- A = (3.14) × (7 units)²
- A = (3.14) × (49 units²)
- A = 153.86 units²
It's important to report our answer in a manner consistent with the significant figures of the given data. As our given diameter is to two significant figures, our final answer should also be given to two significant figures, where necessary. Here, because we used 3.14 for π, our final area measurement is 154 units² when rounded to two significant figures.