Answer:
The height of the second cone is 2 h₁.
Step-by-step explanation:
The volume of a cone is:
[tex]V=\pi\ r^{2}\frac{h}{3}[/tex]
The volume of the first cone is, V₁ = 5 in³.
The volume of the second cone is, V₂ = 10 in³.
The two cones have the same base diameters.
This implies that the two radii are same, i.e. r₁ = r₂.
Compute the height of the second cone as follows:
[tex]r_{1}=r_{2}[/tex]
[tex]\frac{3\cdot V_{1}}{\pi\ h_{1}}=\frac{3\cdot V_{2}}{\pi\ h_{2}}[/tex]
[tex]\frac{V_{1}}{h_{1}}=\frac{V_{2}}{ h_{2}}[/tex]
[tex]\frac{5}{h_{1}}=\frac{10}{h_{2}}[/tex]
[tex]h_{2}=2\ h_{1}[/tex]
Thus, the height of the second cone is 2 h₁.
