Final answer:
The distance a robot's 5" diameter wheel travels in 7 rotations is calculated as 7 times the wheel's circumference, or 7 * 5π, resulting in approximately 110 inches. Due to a discrepancy with the provided options, it appears there may be a typo in the question.
Step-by-step explanation:
To find out how far a robot will travel with a wheel of a certain size, you can use the circumference of the wheel as the distance traveled in one rotation. The circumference (C) is calculated by the formula C = πd, where d is the diameter of the wheel. For a 5" diameter wheel, the circumference is 5π inches.
Therefore, in one rotation, the wheel travels 5π inches. The total distance covered in 7 rotations would be 7 times the distance covered in one rotation, which is 7 * 5π inches. Since π is approximately 3.14159, the distance traveled in 7 rotations is about 7 * 5 * 3.14159 inches, which equals roughly 110 inches. However, this is clearly not an option provided in the question, indicating that there may be a typo in the question. Assuming π is approximated to 3 for simplicity, we can calculate 7 * 5 * 3, which totals to 105 inches, which again, does not match any of the options given. Without rounding, 7 * 5π is approximated as 109.955 inches, but this still does not align with the answer choices.