Step-by-step explanation:
Step 1: Find the radius of the big cone
[tex]\frac{radius_1}{height_1} = \frac{radius_2}{height_2}[/tex]
[tex]\frac{2}{5}=\frac{x}{10}[/tex]
[tex]2(10)=5(x)[/tex]
[tex]20/ 5=5x / 5[/tex]
[tex]4=x[/tex]
Step 2: Find the volume of the small cone
[tex]V = \frac{\pi*r^2*h} {3}[/tex]
[tex]V = \frac{\pi * 2^2 * 5}{3}[/tex]
[tex]V = \frac{20\pi}{3}\ units^3[/tex] ← Volume of Small Cone
Step 3: Find the volume of the large cone
[tex]V = \frac{\pi*r^2*h} {3}[/tex]
[tex]V=\frac{\pi*4^2*10}{3}[/tex]
[tex]V = \frac{160\pi}{3}\ units^3[/tex] ← Volume of Large Cone
