Two similar cones have the following dimensions: Enoch's cone has a radius of 7 cm and a slant height of 15 cm. Alex's cone has a radius of 10.5 cm. What is the slant height of Alex's cone?

For Enoch's cone:
Radius ($r_E$) $= 7$ cm
Slant height ($l_E$) $= 15$ cm

For Alex's cone:
Radius ($r_A$) $= 10.5$ cm
Let the slant height of Alex's cone be $l_A$.

For similar cones, the ratio of corresponding linear dimensions is equal. This means the ratio of their radii is equal to the ratio of their slant heights.

$$\frac{r_A}{r_E} = \frac{l_A}{l_E}$$

First, calculate the ratio of the radii:

$$\frac{10.5}{7} = 1.5$$

Now, substitute this value back into the equation:

$$1.5 = \frac{l_A}{15 \text{ cm}}$$

Multiply both sides by 15 cm to find $l_A$:

$$l_A = 1.5 \times 15 \text{ cm}$$ $$l_A = 22.5 \text{ cm}$$

The slant height of Alex's cone is $\text{22.5 cm}$.