Question

a wheel with a radius of 14 inches rolls along a straight path. how many complete rotations must it make to cover a distance of at least 200 feet? (use $pi=\frac{22}{7}$)
o a. 27
o b. 28
o c. 55
o d. 56

Explanation:

Step1: Calculate the circumference of the wheel

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 14$ inches and $\pi=\frac{22}{7}$, then $C=2\times\frac{22}{7}\times14= 2\times22\times2 = 88$ inches.

Step2: Convert the target - distance to inches

Since 1 foot = 12 inches, a distance of 200 feet is $200\times12=2400$ inches.

Step3: Calculate the number of rotations

The number of rotations $n=\frac{\text{total distance}}{\text{circumference}}=\frac{2400}{88}=\frac{300}{11}\approx27.27$.

Answer:

B. 28