Three tin containers are geometrically similar. The heights of tin container A and tin container C are 8 cm and 16 cm respectively.

1. Find the linear scale factor from tin container C to tin container B using the base area ratio.

For geometrically similar containers,
$\frac{\text{base area of B}}{\text{base area of C}}=\left(\frac{\text{height of B}}{\text{height of C}}\right)^2$
Given
$\frac{\text{base area of B}}{\text{base area of C}}=\frac{25}{64},$
so
$\frac{\text{height of B}}{\text{height of C}}=\sqrt{\frac{25}{64}}=\frac{5}{8}.$

2. Use the height of tin container C to calculate the height of tin container B.

Height of C $=16$ cm.

$\text{Height of B}=\frac{5}{8}\times 16=10\text{ cm}$

1. Find the linear scale factor from tin container C to tin container A.

Heights of A and C are $8$ cm and $16$ cm respectively.

Linear scale factor from C to A:
$\frac{8}{16}=\frac{1}{2}$

2. Use the cube of the linear scale factor to find the weight of tin container A.

For geometrically similar solids,
$\text{volume ratio} = \left(\text{linear scale factor}\right)^3$

Assuming weight is proportional to volume,
$\text{weight of A}=450\left(\frac{1}{2}\right)^3$
$=450\times \frac{1}{8}$
$=56.25$