Final Answer:
The radius of the sphere is approximately 39 cm (Option 3).
Step-by-step explanation:
The formula for the circumference of a sphere is C = 2πr, where C is the circumference and r is the radius. Given the circumference of the sphere as 78 cm with a possible error of ±0.5 cm, we can use this information to determine the range of possible values for the radius.
The measured circumference is 78 cm, and the maximum possible circumference would be 78 cm + 0.5 cm = 78.5 cm, while the minimum possible circumference would be 78 cm - 0.5 cm = 77.5 cm. Using the formula C = 2πr, we can solve for the radius by rearranging the formula: r = C / (2π). Substituting the maximum and minimum circumferences into the formula gives us the maximum and minimum possible radii.
Calculating the radius for the maximum possible circumference, r_max = 78.5 / (2π) ≈ 39.5 / π ≈ 12.57 cm, and for the minimum possible circumference, r_min = 77.5 / (2π) ≈ 12.35 cm. Therefore, the radius of the sphere falls within the range of approximately 12.35 cm to 12.57 cm. Rounding to the nearest whole number, the closest option is 39 cm, making it the most accurate approximation for the radius of the sphere within the given range of possible errors in the measurement of the circumference.Option 3