Answer :
Option C:
Height of the smaller cone is[tex]\frac{15}{7}[/tex] .
Solution:
Height of the larger cone = 5
Radius of the larger cone = 7
Radius of the smaller cone =3
To find the height of the smaller cone:
If two polygons are similar, then the corresponding sides are proportional to each other.
[tex]$\Rightarrow\frac{5}{x} =\frac{7}{3}[/tex]
Do cross multiplication.
[tex]$\Rightarrow5\times3=7x[/tex]
⇒ 15 = 7x
[tex]$\Rightarrow\frac{15}{7}=x[/tex]
[tex]$\Rightarrow x=\frac{15}{7}[/tex]
Option C is the correct answer.
Height of the smaller cone is[tex]\frac{15}{7}[/tex] .