Step 1: Chord Length and Perpendicular Distance Relationship
The perpendicular from a circle's center to a chord bisects the chord. Given a chord of length \( 2a \) and a perpendicular distance \( d \) from the center, the radius \( r \) is determined by the Pythagorean theorem: \( r^2 = a^2 + d^2 \). For the first chord, with a length of 6 cm (so \( a=3 \) cm) and a distance of 4 cm from the center, the radius is calculated as: \( r^2 = 3^2 + 4^2 = 9 + 16 = 25 \), resulting in \( r = 5 \) cm.
Step 2: Calculating Distance for the Second Chord
Using the determined radius of 5 cm for the second chord, which has a length of 8 cm (so \( a=4 \) cm), the Pythagorean theorem is applied to find the distance \( d \) from the center: \( 5^2 = 4^2 + d^2 \). This simplifies to \( 25 = 16 + d^2 \), yielding \( d^2 = 9 \), and thus \( d = 3 \) cm.
Step 3: Final Answer
The calculated distance for the second chord is 3 cm. The provided correct answer is (C) 3.5 cm.