In a circle of radius 6cm a chord is drawn 3cm from the center.

To find the angle subtended by the chord at the center of the circle, we can use the formula:

Angle = 2 * arcsin(chord length / (2 * radius))

Here, the chord length is 3cm and the radius is 6cm.
Angle = 2 * arcsin(3 / (2 * 6))
Angle = 2 * arcsin(1/4)
Angle = 2 * 14.48 degrees
Angle = 28.96 degrees

Therefore, the angle subtended by the chord at the center of the circle is 28.96 degrees.

To find the length of the minor arc cut off by the chord, we can use the formula:

Arc length = 2 * pi * radius * (angle/360)

Arc length = 2 * 3.14 * 6 * (28.96 / 360)
Arc length = 2 * 3.14 * 6 * 0.0804
Arc length = 2.42 cm

Therefore, the length of the minor arc cut off by the chord is 2.42 cm.