Four Cubes
Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?
Age
14 to 16
Challenge level
Problem
Image
What is the surface area of this cuboid, in $\text{cm}^2$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Each of the cubes has $6$ faces, and a total surface area of $24\text{cm}^2$.
The area of each face is then $24\text{cm}^2 \div 6 = 4\text{cm}^2$.
The cuboid has sixteen of these faces showing, which gives a total surface area of $16 \times 4\text{cm}^2 = 64\text{cm}^2$.
Alternatively, if each face of each cube has area $4\text{cm}^2$, each cube has side length $2\text{cm}$. This means the cuboid is $4\text{cm} \times 4\text{cm} \times 2\text{cm}$.
The surface area is then: $2 \times 4\text{cm} \times 4\text{cm} + 4 \times 4\text{cm} \times 2\text{cm} = 32\text{cm}^2 + 32\text{cm}^2 = 64\text{cm}^2$.