A and B are solids which are mathematically similar. The length of A is 4cm and the length of B is 12cm. If the volume of A is 3cm cubed, what is the volume of solid B?


Since the solids A and B are mathematically similar, their volumes are proportional to the cube of their corresponding lengths.

The ratio of the lengths of A and B is:

\[
\text{Length ratio} = \frac{\text{Length of B}}{\text{Length of A}} = \frac{12}{4} = 3
\]

Since the volumes are proportional to the cube of the lengths, the volume ratio is:

\[
\text{Volume ratio} = \left( \frac{\text{Length of B}}{\text{Length of A}} \right)^3 = 3^3 = 27
\]

Thus, the volume of solid B is 27 times the volume of solid A:

\[
\text{Volume of B} = 27 \times \text{Volume of A} = 27 \times 3 = 81 \, \text{cm}^3
\]

So, the volume of solid B is **81 cm³**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the surface areas of A and B compare?
2. If the area of one face of A is known, how would you calculate the area of the corresponding face of B?
3. What if the length of B was 8 cm? What would the volume of B be?
4. How would the mass of solid B compare to A if their densities are the same?
5. How does the relationship between dimensions and volume change in non-similar shapes?

**Tip**: For geometrically similar shapes, all corresponding linear dimensions are proportional, and volumes scale with the cube of the scale factor!

A and B are solids which are mathematically similar. The length of A is 4cm and the length of B is 12cm. If the volume of A is 3cm cubed, what is the volume of solid B?

Learn how to calculate the volume of solid B using the length ratio of mathematically similar solids. If solid A has a length of 4cm and a volume of 3cm³, and solid B has a length of 12cm, find the volume of B. This problem covers volume scaling, ratios, and proportional relationships in geometry. Suitable for students in Grades 8-10.

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