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

Question

asked Oct 13, 2020 226k views

1 Answer

Dalvenjia · Answer 1 · 2020-10-19T17:27:39+0000

Answer:

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

the height of the cup is
$6\ in$

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)

$54=(x^(3))/(4) \\ \\x^(3)=216\\ \\x=6\ in$

therefore

The radius of the cup is

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

The height of the cup is

$h=6\ in$