Question

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

A. 35/3
B. 21/5
C. 5
D. 15/7

Answer 1

Answer: The correct option is (D)
`(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

`(5)/(x)=(7)/(3)\\\\\\\Rightarrow 5* 3=7x\\\\\\\Rightarrow7x=15\\\\\\\Rightarrow x=(15)/(7).`

Thus, the height of the smaller cone is
`(15)/(7)~\textup{units}.`

Option (D) is correct.

Answer 2

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