Answer:
The radius of the cup is [tex]3\ in[/tex] and
the height of the cup is [tex]6\ in[/tex]
Step-by-step explanation:
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
Let
x-----> the height and the diameter of the cylinder
we have
[tex]V=54\pi\ in^{3}[/tex]
[tex]h=x\ in[/tex]
[tex]D=x\ in[/tex]
[tex]r=(x/2)\ in[/tex]
substitute the values
[tex]54\pi=\pi (x/2)^{2}(x)[/tex]
simplify
[tex]54=(x/2)^{2}(x)[/tex]
[tex]54=\frac{x^{3}}{4} \\ \\x^{3}=216\\ \\x=6\ in[/tex]
therefore
The radius of the cup is
[tex]r=(6/2)=3\ in[/tex]
The height of the cup is
[tex]h=6\ in[/tex]
