Question

The volume of a cylinder is 4pi x(3) cubic units and its height is x units. Which expression represents the radius of the cylinder in units? 2x, 4x, 2 pi x^, 4 pi x^

Answer 1

2x

Explanation:

Volume of a cylinder is:

V = πr²h

If V = 4πx³ and h = x, then:

4πx³ = πr²x

4x² = r²

r = 2x

Answer 2

For this case we have that by definition, the volume of a cylinder is given by:

`V = \pi * r ^ 2 * h`

Where:

r: It's the radio

h: It's the height

We have as data that the volume of the cylinder is:

`V = 4 \pi * x ^ 3`

They also tell us that the height is "x", then:

`4 \pi * x ^ 3 = \pi * r ^ 2 * x`

We have similar terms on both sides of the equation:

`4x ^ 2 = r ^ 2`

We apply root to both sides of the equation:

`r = \pm \sqrt {4x ^ 2}\\r = \pm2x`

We choose the positive value. Now the radio is 2x

Answer:

`2x`