图中显示了两个几何相似的容器。给较小容器的底面积涂漆的费用是给较大容器底面积涂漆费用的 $\frac{25}{64}$。

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,
$1.8432 \approx 1.84.$