For a certain sphere the number measuring its volume in ${\text{cm}}^3$ is equal to the number measuring its surface area in ${\text{cm}}^2$. Find its radius in cm.

(4/3)π$r^3=4$π$r^2$ gives $r/3=1$, so $r=3$ cm. Check: volume = 36π and surface area = 36π. (Cancelling carelessly to $r^3=r^2$ gives $r=1$, which fails the check — that sphere has volume 4π/3 but surface area 4π.)