Answer: The correct option is (D) \(\dfrac{15}{7}.\)
Step-by-step explanation: Given that the two cones in the figure are similar.
We are to find the height 'x' of the smaller cone.
The height and radius of the bigger cone are 5 units and 7 units respectively.
The radius of the smaller cone is 3 units.
Since the two cones are similar, so their corresponding heights and radius will be proportional.
Therefore, we must have
\(\dfrac{5}{x}=\dfrac{7}{3}\\\\\\\Rightarrow 5\times 3=7x\\\\\\\Rightarrow7x=15\\\\\\\Rightarrow x=\dfrac{15}{7}.\)
Thus, the height of the smaller cone is \(\dfrac{15}{7}~\textup{units}.\)
Option (D) is correct.
