A cube is placed on top of a cuboid, as shown in the diagram, to form a solid - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 1

The surface area (SA) of a cube is calculated using the formula: $SA = 6a^2$ where:

• $a = 4 \text{ cm}$

Calculating: $SA_{cube} = 6 \cdot (4)^2 = 6 \cdot 16 = 96 \text{ cm}^2$

The top face of the cuboid, which is covered by the cube, is not included in the total surface area. The area of this face is: $Area_{overlap} = l \cdot w = 7 \cdot 6 = 42 \text{ cm}^2$

Now, combine the surfaces, subtracting the overlapping area: $Total \: SA = SA_{cuboid} + SA_{cube} - Area_{overlap}$ $Total \: SA = 214 + 96 - 42 = 268 \text{ cm}^2$