The following diagram shows 2 geometrically similar boxes of cereals of the same brand.

1. Compare the unit costs to test direct proportionality

For Box A,
$\frac{0.80}{20}=0.04$
Cost per gram $= \char36{}0.04$ per g.

For Box B,
$\frac{3.40}{160}=0.02125$
Cost per gram $= \char36{}0.02125$ per g.

Since $0.04 \ne 0.02125$, the cost per gram is not constant. Therefore, the cost is not directly proportional to the quantity.

1. Use the quantity ratio to find the linear height ratio

The boxes are geometrically similar, so
$\frac{\text{volume of A}}{\text{volume of B}}=\left(\frac{\text{height of A}}{\text{height of B}}\right)^3.$
Using the given quantities,
$\frac{20}{160}=\frac{1}{8}.$
Hence,
$\left(\frac{\text{height of A}}{\text{height of B}}\right)^3=\frac{1}{8},$
so
$\frac{\text{height of A}}{\text{height of B}}=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}.$

1. Convert the linear ratio into the surface area ratio

From part (b),
$\frac{\text{height of Box A}}{\text{height of Box B}}=\frac{1}{2}.$
Since the boxes are geometrically similar,
$\frac{\text{surface area of Box A}}{\text{surface area of Box B}}=\left(\frac{1}{2}\right)^2=\frac{1}{4}.$

2. Calculate the surface area of Box B

$\frac{454}{\text{surface area of Box B}}=\frac{1}{4}$
$\text{surface area of Box B}=454\times 4=1816$