Problem: A wheel with a rubber tire has an outside diameter of 25 in . When the radius has been decreased a quarter of an inch, the number of revolutions of the wheel in one mile will:
Answer Choices:
A. be increased about 2%
B. be increased about 1%
C. be increased about 20%
D. be increased by 1/2%
E. remain the same
Solution:
N1​=πD1 mile ​,N2​=π[D−(1/2)]1 mile ​,N2​−N1​=π1 mile ​⋅D[D−(1/2)]1/2​.
∴N1​N2​−N1​​=D−1/21/2​=2421​1/2​=491​;
∴ the percent increase is 100⋅491​∼2%.