A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is

To divide a 3D cube into smaller pieces of equal size and shape using straight, complete through-cuts:

1. Let the number of cuts along the three mutually perpendicular directions ($x$, $y$, and $z$ axes) be $c_x$, $c_y$, and $c_z$.

2. The total number of pieces produced is:

   $$\text{Total pieces} = (c_x + 1)(c_y + 1)(c_z + 1)$$

3. We are given that the number of pieces is $8$:

   $$(c_x + 1)(c_y + 1)(c_z + 1) = 8$$

4. To minimize the total number of cuts $C = c_x + c_y + c_z$, the factors $(c_x + 1)$, $(c_y + 1)$, and $(c_z + 1)$ should be made as equal as possible:

   $$8 = 2 \times 2 \times 2$$

   Setting $c_x + 1 = 2 \implies c_x = 1$, $c_y + 1 = 2 \implies c_y = 1$, and $c_z + 1 = 2 \implies c_z = 1$.

5. Therefore, the minimum number of cuts required is:

   $$C_{\text{min}} = 1 + 1 + 1 = 3$$

Thus, the correct option is (A).