Answer:
Correct answer is D
Step-by-step explanation:
Two similar cones have radii of [tex]R=6[/tex] units and [tex]r=1[/tex] unit. Then the coefficient of similarity is
[tex]k=\dfrac{R}{r}=\dfrac{6}{1}=6.[/tex]
The similar shapes have all linear lengths proportional. If H is the height of the larger cone and h is the height of the smaller cone, then
[tex]\dfrac{H}{h}=k,\\ \\\dfrac{H}{h}=6\Rightarrow H=6h.[/tex]
Use formula for the volume of the cone:
[tex]V_{cone}=\dfrac{1}{3}\cdot \pi r^2\cdot h.[/tex]
Then
[tex]\dfrac{V_{\text{large cone}}}{V_{\text{smal cone}}}=\dfrac{\frac{1}{3}\cdot \pi R^2\cdot H}{\frac{1}{3}\cdot \pi r^2\cdot h}=\dfrac{(6)^2\cdot 6h}{1^2\cdot h}=\dfrac{36\cdot 6}{1}=\dfrac{216}{1}.[/tex]
