A

Step 1: Understand the system. We have a cube with mass \( m = 3 \, \text{kg} \) on a frictionless surface. Point A of the cube is moving with a velocity of \( v_A = 4 \, \text{m/s} \). The distance between points A and B is given as \( 10 \, \text{cm} = 0.1 \, \text{m} \).

Step 2: Determine speed of point B. Since point A moves forward, point B will also have some velocity due to rotational motion. The speed of point B is stated to be \( 4 \, \text{m/s} \).

Step 3: Calculate the kinetic energy of the cube. The formula for kinetic energy is given by:
$$ KE = \frac{1}{2} m v^2 $$
where \( v \) is the speed of the center of mass of the cube (which is just the speed of point A since the surface is frictionless). Thus, we find the kinetic energy of the block as follows:
$$ KE = \frac{1}{2} \times 3 \, \text{kg} \times (4 \, \text{m/s})^2 = \frac{1}{2} \times 3 \times 16 = 24 \, \text{J} $$
Therefore, the kinetic energy of the block is \( 24 \, \text{J} \).