Given two similar solid cylinders with volumes 4096 cm³ and 1728 cm³, find the height of the larger cylinder if the smaller cylinder has a height of 12 cm.

4. Similar Solid Cylinders and Composite Solid Volume

a) Find the height of the larger cylinder.

Step 1: Determine the ratio of the volumes of the two similar cylinders.
Let $V_L$ be the volume of the larger cylinder and $V_S$ be the volume of the smaller cylinder.

$$V_L = 4096 \text{ cm}^3$$ $$V_S = 1728 \text{ cm}^3$$

The ratio of volumes is:

$$\frac{V_L}{V_S} = \frac{4096}{1728}$$

Simplify the ratio:

$$$$