Question

The two cones below are similar. What is the height of the smaller cone?

Answer 1

Given that the two cone are similar, then
3/7 = x/5
7x = 15
x = 15/7

Answer 2

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.