The base radius and the vertical height of a cone are in the ratio 3 : 4, and its volume is $301.44{\text{cm}}^3$. Find its base radius in cm. Take π = 3.14.

Write $r=3k$ and $h=4k$. Then $(1/3)(3.14)(9k^2)(4k)=37.68k^3=301.44$, so $k^3=8$ and $k=2$. Hence $r=3\times 2=6$ cm (and $h=8$ cm). (8 cm is the height, 10 cm is the slant height √(36 + 64) that this cone also happens to have, and 3 cm is the multiplier's partner $k=2$ confused with the bare ratio number 3.)