Two similar cones have radii 3 cm and 9 cm. a) Find the scale factor. b) If the smaller cone has volume 40 cm3, find the volume of the larger cone.

4. Two similar cones have radii 3 cm and 9 cm.
Let $r_1 = 3$ cm (smaller cone) and $r_2 = 9$ cm (larger cone).

4.a) Find the scale factor.
The scale factor $k$ is the ratio of corresponding linear dimensions. We'll use the ratio of the larger radius to the smaller radius.

$$k = \frac{r_2}{r_1} = \frac{9 \text{ cm}}{3 \text{ cm}} = 3$$

The scale factor is $\boxed{3}$.

4.b) If the smaller cone has volume 40 cm$^3$, find the volume of the larger cone.
For similar solids,