ANSWER
[tex]h= 4in.[/tex]
EXPLANATION
The volume of a cylinder is calculated using the formula;
[tex]v = \pi \: {r}^{2} h[/tex]
It was given that, the cylinder has a radius of 2 inches and a height of 3 inches.
This implies that,
[tex]v = \pi \times {2}^{2} \times 3[/tex]
[tex]v =12 \pi [/tex]
The volume of a cone is given by
[tex]v = \frac{1}{3} \times \pi {r}^{2} h[/tex]
The cone has a radius of 3 inches:
[tex]v=\frac{1}{3} \times \pi \times {3}^{2} h[/tex]
[tex]v=3 \pi h[/tex]
The two volumes are the same:
This implies that,
[tex]3 \pi h = 12\pi[/tex]
Divide both sides by 3π
[tex] h= 4in[/tex]
