Final answer:
To calculate the area of the circle that circumscribes an equilateral triangle with a radius of 10 cm, we use the formula A = πr², which yields approximately 314.15927 cm². This answer should be rounded to two significant figures, giving an area of 310 cm².
Step-by-step explanation:
The student is asking for the area of the circle that circumscribes an equilateral triangle with a given radius of 10 cm. To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius of the circle. Plugging the given radius into the formula, we have:
A = π(10 cm)²
A = π (100 cm²)
A = 314.15927 cm²
Since the provided radius has two significant figures, the area should also be presented with two significant figures:
A = 310 cm² (to two significant figures)
This provides us with the approximate area of the circle in square centimeters.