Which of the two containers would carry more: a square box with sides of 200mm each, or a rectangular box with sides of 80mm each and a length of 800mm?

This equals the internal volume of the bowl or vase.

Units: Volume in cm³ or mL (1 cm³ = 1 mL), depending on the measuring cylinder.

Formula: $V_1 = s^3$, where $s = 200$ mm.

$$V_1 = 200 \times 200 \times 200~\text{mm}^3$$ $$200 \times 200 = 40{,}000$$ $$40{,}000 \times 200 = 8{,}000{,}000~\text{mm}^3$$

Formula: $V_2 = w \times h \times l$, where $w = 90$ mm, $h = 90$ mm, $l = 800$ mm.

$$V_2 = 90 \times 90 \times 800~\text{mm}^3$$ $$90 \times 90 = 8{,}100$$ $$8{,}100 \times 800 = 8{,}100 \times 8 \times 100 = 64{,}800 \times 100 = 6{,}480{,}000~\text{mm}^3$$

divide by 1{,}000).

$$V_1 = 8{,}000{,}000~\text{mm}^3 = 8{,}000~\text{cm}^3$$ $$V_2 = 6{,}480{,}000~\text{mm}^3 = 6{,}480~\text{cm}^3$$

$V_1 > V_2$.

The square box carries more volume.
V_{square box} = 8{,}000{,}000 mm^{3}
V_{rectangular box} = 6{,}480{,}000 mm^{3}
(square box > rectangular box)