Question

The height and diameter of a cylindrical cup are the same length. The volume of the cup is 54pi in3 what is the radius and the height of the cup

Answer 1

Answer:

The radius of the cup is $3\ in$ and

the height of the cup is $6\ in$

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

$V=\pi r^{2}h$

Let

x-----> the height and the diameter of the cylinder

we have

$V=54\pi\ in^{3}$

$h=x\ in$

$D=x\ in$

$r=(x/2)\ in$

substitute the values

$54\pi=\pi (x/2)^{2}(x)$

simplify

$54=(x/2)^{2}(x)$

$54=\frac{x^{3}}{4} \\ \\x^{3}=216\\ \\x=6\ in$

therefore

The radius of the cup is

$r=(6/2)=3\ in$

The height of the cup is

$h=6\ in$