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 formula for the total surface area (SA) of a cube is:

$SA = 6a^2$

where:

• a = edge length = 4 cm

Calculating:

$SA_{cube} = 6(4^2)$ $= 6(16)$ $= 96 \, cm^2$

To find the total surface area of the solid, we need to add the surface areas of the cube and the cuboid, adjusting for the area of the top face of the cuboid that is in contact with the cube.

• Area of the top face of the cuboid = length × width = 7 cm × 6 cm = 42 cm²

Now, subtract this area from the total:

$SA_{total} = SA_{cuboid} + SA_{cube} - Area_{top face}$

$SA_{total} = 214 + 96 - 42$ $= 268 \, cm^2$