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Answer :
Final answer:
The area of a circle with a radius of 4 meters is best estimated to be 50.2 m², after rounding to two significant figures to match the precision of the given radius value.
Explanation:
You're looking for a measurement that is a good estimate for the area of a circle with a radius of 4 meters. To estimate the area, you use the formula A = πr², where A is the area, π (pi) is approximately 3.1415927, and r is the radius of the circle. Using this formula, you calculate the area as follows: A = π × (4 m)² = 3.1415927 × 16 m² = 50.26548256 m². However, since the radius is given with two significant figures, the area should also be reported with two significant figures. Therefore, the best estimate for the area would be 50.2 m².
It's important to consider units carefully. In this case, since we're dealing with area, our units are in square meters. A mistake some might make is to approximate the area of a circle by assuming it's close to that of a square with the same diameter. However, the area of the circle will always be less. If you have a square with a side length of 8 meters (which is the diameter of the circle), the area of that square is 64 m², but the circle fits inside the square, so its area is less. Indeed, the circle's area is approximately π times the radius squared, which is less than the square's area.
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