Question 14
A rectangular box (cuboid) is to be built by stacking small cubes with edge $1~\mathrm{cm}$; its length consists of $n$ small cubes, its width of $p$ small cubes and its height of $q$ small cubes.
a) What is the volume of the box?
b) If the faces of the box are painted red, how many small cubes will have exactly one of their faces painted red?
c) Take a box as in the statement with $n=p=q$. If we increase each of its dimensions by $a$, where $a$ is a natural number, the new cube has 98 small cubes more than the initial cube. What are the values of $n$ and $a$?
a) What is the volume of the box?
b) If the faces of the box are painted red, how many small cubes will have exactly one of their faces painted red?
c) Take a box as in the statement with $n=p=q$. If we increase each of its dimensions by $a$, where $a$ is a natural number, the new cube has 98 small cubes more than the initial cube. What are the values of $n$ and $a$?