Below are two similar vases. The volume of the smaller vase is 0.8 litres. What is the volume of the larger vase?

If the two vases are similar, their shapes are geometrically similar, meaning that all corresponding dimensions are proportional. The ratio of their volumes is the cube of the ratio of their corresponding linear dimensions (such as height or radius). 

Let’s denote:
- \( V_s = 0.8 \) liters as the volume of the smaller vase.
- \( V_l \) as the unknown volume of the larger vase.
- \( r_s \) and \( r_l \) as the corresponding linear dimensions (such as the height or radius) of the smaller and larger vases, respectively.

Since the volumes of similar objects are proportional to the cube of their linear dimensions:

\[
\frac{V_l}{V_s} = \left( \frac{r_l}{r_s} \right)^3
\]

To find the volume of the larger vase, we need the ratio \( \frac{r_l}{r_s} \), which represents how much larger the linear dimensions of the larger vase are compared to the smaller one. If you provide this ratio or more information about their dimensions, we

Discover how to calculate the volume of a larger vase when given the volume of a smaller vase using the concept of geometrically similar figures. This problem explores the relationship between the volumes and corresponding linear dimensions of similar objects, suitable for students in Grades 8-10.

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