Question 33

The length of plastic barrier needed is 15.7 feet.

To enclose a circular flower bed with a 5-foot diameter, the circumference can be calculated using the formula \( C = \pi \times d \). Substituting the values gives \( C = 3.14 \times 5 = 15.7 \) feet.

A) 19.625 feet

This option is incorrect because it suggests a circumference that is larger than what is calculated using the diameter provided. The correct application of the circumference formula does not support this length.

B) 15.7 feet

This is the correct answer, as it accurately represents the circumference calculated using the formula \( C = \pi \times d \) with \( d = 5 \) feet and \( \pi = 3.14 \).

C) 31.4 feet

This option is also incorrect. It represents the circumference of a circle with a diameter of 10 feet rather than the 5-foot diameter specified in the question. Therefore, it does not align with the required calculation.

D) 7.85 feet

This option is incorrect because it indicates a circumference that is half of the actual calculation. The correct formula yields a larger value, making this option invalid.

Conclusion

The correct length of the plastic barrier needed to enclose the circular flower bed is 15.7 feet, as derived from the proper application of the circumference formula. All other options fail because they either miscalculate or misrepresent the dimensions provided in the question.