Skip over navigation
Let the smaller cubes have side length $1\,\mathrm{unit}$. So the original cube had side of length $3\,\mathrm{units}$ and as a cube has six faces it had a surface area of
$$6\times(3\,\mathrm{units}\times 3\,\mathrm{units})=54\,\mathrm{units}^2\;,$$
all of which was painted blue.
The total surface are of the 27 small cubes is
$$27\times 6\,\mathrm{units}^2 = 162\,\mathrm{units}^2\;.$$
So the required fraction is
$$\frac{54\,\mathrm{units}^2}{162\,\mathrm{units}^2} = \frac{1}{3}\;.$$
Cubic Masterpiece
Age 11 to 14
ShortChallenge Level 
Let the smaller cubes have side length $1\,\mathrm{unit}$. So the original cube had side of length $3\,\mathrm{units}$ and as a cube has six faces it had a surface area of
$$6\times(3\,\mathrm{units}\times 3\,\mathrm{units})=54\,\mathrm{units}^2\;,$$
all of which was painted blue.
The total surface are of the 27 small cubes is
$$27\times 6\,\mathrm{units}^2 = 162\,\mathrm{units}^2\;.$$
So the required fraction is
$$\frac{54\,\mathrm{units}^2}{162\,\mathrm{units}^2} = \frac{1}{3}\;.$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
You may also like
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Days and Dates
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...