Rotating cone

How does the volume of the rotating cone change if:

a) double the radius of the base
b) We reduce the height three times
c) Reduce the radius of the base five times

Correct answer:

k₁ =  4
k₂ =  0.3333
k₃ =  0.04

Step-by-step explanation:

$$\begin{gathered} V=\frac{1}{3}\pi r^{2}h \\ {V}_1=\frac{1}{3}\pi (2r{)}^{2}h \\ {k}_1=V_1/V \\ {k}_1=2^2=4 \end{gathered}$$

$$\begin{gathered} V_2=\frac{1}{3}\pi r^2(h/3) \\ {k}_2=V_2/V \\ {k}_2=1/3=0.3333 \end{gathered}$$

$$\begin{gathered} V_3=\frac{1}{3}\pi (r/5{)}^{2}h \\ {k}_3=V_3/V \\ {k}_3=(1/5{)}^2=0.04 \end{gathered}$$

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