Cuboid cut into cubes

The surface area of a cuboid is given by $S_{cuboid}=2(HW+WL+LH)$ where $H$ = height, $W$ = width and $L$ = length.

Substituting, we get

$S_{cuboid}=2[5(10)+10(15)+15(5)]=550$

The surface area of a cube is given by $S_{cube}=6a^2$ where $a$ = side length of the cube

Substituting, we get

$S_{cube}=6(5^2)=6(25)=150$

Since there are $6$ cubes, we multiply it by $6$ . Therefore, the total surface area of the $6$ cubes is $6(150)=900$ .

Finally, the difference is $900-550=$ $\color{#D61F06}\large \boxed{350}$

The cuboid is divided by cutting the top into a 2x3 grid. There are 7 lines of division. Each line accounts for two cube faces that are obscured in the cuboid shape, but revealed when it is separated. Each face has area 5x5 = 25 square centimetres. Hence 14x25 = 350.

$A_{6 cubes}=$ $(6)(6)(5^2)=900$ $cm^2$

$A_{cuboid}=2[(5)(10)+(15)(5)+(15)(10)] = 550$ $cm^2$

$difference$ $in$ $surface$ $area$ $=$ $900 - 550 = 350$ $cm^2$

6 cubes are formed, each with a side of 5cm.

Let each cube's face be one unit Therefore each cube has a surface area of 6 units 6 units (surface area) X 6 cubes = 36 units

The six faces of the original cuboid (pictured above) have, 2, 2, 3, 3, 6, 6 faces = 22 faces = 22 units.

The difference in units is 36-22=14 units Each unit is 5 cm x 5cm = 25 square cm

14 units X (25 cm^2/unit) = 350 cm^2

$\text{ No. of cubes formed = }$ $\frac{10×15×5}{5×5×5} = 6 \text{cubes}$

$\text{Surface Area of cuboid }= 2 (10×15+15×5+5×10) = 550 \text{ cm}^2$

$\text{Surface Area of each Cube} = 6 × 5^2 = 150 \text{ cm}^2$

$\text{Sum of Surface Areas of all cubes} = 6 × 150 =900 \text{ cm}^2$

$\text{Required Difference} = 900-550 = \boxed{ \large \color{#D61F06}{350}}$