The proportion of radius will be the same with the proportion of the height. Make a comparison
[tex]\cfrac{h_{1}}{h_{2}}=\cfrac{r_{1}}{r_{2}}[/tex]
Input the numbers
[tex]\cfrac{h_{1}}{h_{2}}=\cfrac{40}{16} [/tex]
simplify the fraction, divide the numerator and denominator by 8
[tex]\cfrac{h_{1}}{h_{2}}=\cfrac{5}{2} [/tex]
do cross multiplication
2h₁ = 5h₂
h₂ = [tex] \frac{2}{5}h_{1} [/tex]
General formula to find the volume
1/3 × π × r² × h = volume
In the case of the first cone
1/3 × π × 40² × h₁ = 1,875
1/3 × π × 1,600 × h₁ = 1,875
1/3 × π × h₁ = [tex] \frac{1,875}{1,600} [/tex]
save it, we'll use this expression later
In the case of the second cone
We know that h₂ = [tex] \frac{2}{5}h_{1} [/tex]
So the expression will be
1/3 × π × r₂² × h₂ = v₂
1/3 × π × 16² × h₂ = v₂
1/3 × π × 256 × [tex] \frac{2}{5}h_{1} [/tex] = v₂
1/3 × π × h₁ × [tex] \frac{256 \times 2}{5} [/tex] = v₂
1/3 × π × h₁ × [tex] \frac{512}{5} [/tex] = v₂
Use the expression we save, substitute 1/3 × π × h₁ with [tex] \frac{1,875}{1,600} [/tex]
[tex]\frac{1,875}{1,600} \times\frac{512}{5}[/tex] = v₂
120 = v₂
The volume of the second cone is 120 cm³
