The diagram shows two geometrically similar containers. The cost of painting the base area of the smaller container is $\frac{25}{64}$ of the cost of painting the base of the larger container.

1. Find the linear scale factor from the area ratio.

The cost of painting the base is proportional to the base area.

So,
$\frac{\text{base area of smaller}}{\text{base area of larger}}=\frac{25}{64}.$

For similar figures,
$\frac{\text{length of smaller}}{\text{length of larger}}=\sqrt{\frac{25}{64}}=\frac{5}{8}.$

2. Apply the linear scale factor to the circumference.

Circumference is a length, so it uses the linear scale factor.

$\text{circumference of smaller top}=\frac{5}{8}\times 24=15.$

1. Use the volume ratio of similar solids to find the larger capacity.

From part (a), the linear scale factor
$\text{smaller} : \text{larger} = 5 : 8.$
For similar containers,
$\text{volume ratio} = 5^3 : 8^3 = 125 : 512.$
So
$\text{larger capacity}=0.45\times \frac{512}{125}=1.8432.$
To 2 decimal places,
$1.8432 \approx 1.84.$