A grain hopper is an upside-down pyramid: its open top is a square of side 6 $m$ and it narrows to a point 4.5 $m$ below. Find its capacity in $m^3$.

A pyramid holds (1/3) × base area × height, and the base here is the square top: $(1/3)\times 6^2\times 4.5=(1/3)\times 36\times 4.5=54m^3$. (Treating it as a box gives $162{\text{m}}^3$; using ½ in place of ⅓ gives $81{\text{m}}^3$; halving the side to 3 $m$ before squaring gives $13.5{\text{m}}^3.$)