Question

Two similar cones have radii of 6 and 1, respectively. What is the ratio of their volumes?

Answer 1

The answer is D:216:1 good luck with apex

Answer 2

Answer:

Correct answer is D

Step-by-step explanation:

Two  similar cones have radii of $R=6$ units and $r=1$ unit. Then the coefficient of similarity is

$k=\dfrac{R}{r}=\dfrac{6}{1}=6.$

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

$\dfrac{H}{h}=k,\\ \\\dfrac{H}{h}=6\Rightarrow H=6h.$

Use formula for the volume of the cone:

$V_{cone}=\dfrac{1}{3}\cdot \pi r^2\cdot h.$

Then

$\dfrac{V_{\text{large cone}}}{V_{\text{smal cone}}}=\dfrac{\frac{1}{3}\cdot \pi R^2\cdot H}{\frac{1}{3}\cdot \pi r^2\cdot h}=\dfrac{(6)^2\cdot 6h}{1^2\cdot h}=\dfrac{36\cdot 6}{1}=\dfrac{216}{1}.$