Question

The radius of track A is 14 m. If the initial separation between Ted and Ned is 22 m, find the circumference of track C if the radius of the tracks increase uniformly.

• A. 122 m
• B. 110 m
• C. 128 m
• D. 132 m

Answer 1

The correct option is D

132 m

The circumference of track A = 2 $\pi$ r = 2 $\times$ (22/7) $\times$ 14 = 88 m

The circumference of track B = circumference of track A + 22 m = (88 + 22) m = 110 m

Let the radius of track B be r’. So, circumference of track B = 2 $\pi$ r’

2 $\pi$ r’ = 110 m

2 $\times$ (22/7) $\times$ r’ = 110

r’ = 17.5 m

Increase in radius = (17.5 - 14) = 3.5 m

So, radius of track C = r” =(17.5 + 3.5) m = 21 m

Circumference of track C = 2 $\pi$ r” = 2 $\times$ (22/7) $\times$ 21 = 132 m