Question

Find the surface area of a box height h whose base dimensions are p and q, and satisfies each of the following conditions:
a)The box is closed
b)The box has an open top
c)The box has an open top and a square base with side length p

Answer 1

Draw a diagram for this, it will help you visualize everything. So we know that the height of the box = h and the base has sides of length p and q.
This means that the base has an area of p*q
Since it's a box, the top and bottom are the same so we have 2*p*q
Two sides of the box have width p, so the area for the two is 2*p*h and similarly for the other two sides we get 2*q*h. Summing these all together gives
2(pq+ph+qh) = total surface area when the box is closed