If the areas of two similar figures are 36 cm2 and 25 cm2, what is the ratio of their volumes?

For any two similar figures, if the ratio of their corresponding linear dimensions is $k$, then the ratio of their areas is $k^2$, and the ratio of their volumes is $k^3$.
Given the areas of two similar figures (even if the question states "triangles," it implies similar 3D figures whose corresponding 2D areas are given), we can find the linear scale factor.

Let $A_1$ and $A_2$ be the areas, and $V_1$ and $V_2$ be the volumes.
We are given $A_1 = 36 \text{ cm}^2$ and $A_2 = 25 \text{ cm}^2$.

The ratio of the areas is:

$$\frac{A_1}{A_2} = \frac{36}{25}$$

Since the ratio of areas is equal to the square of the linear scale factor ($k^2$), we have:

$$k^2 = \frac{36}{25}$$

To find the linear scale factor $k$, take the square root of both sides:

$$k = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5}$$

The ratio of the volumes of similar figures is equal to the cube of the linear scale factor ($k^3$):

$$\frac{V_1}{V_2} = k^3 = \left(\frac{6}{5}\right)^3$$ $$\frac{V_1}{V_2} = \frac{6^3}{5^3} = \frac{216}{125}$$

The ratio of their volumes is $216:125$.