Question

The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units. What is the height of the cylinder? 2 units 4 units 6 units 8 units

Answer 1

`\boxed{6 \: \mathrm{units}}`

Explanation:

The formula for volume of cylinder is:

`V=\pi r^2 h\\V:volume\\r:radius\\h:height`

`V=24\pi\\h=3r`

Solve for r.

`24\pi =\pi r^2 (3r)`

Cancel
`\pi` on both sides.

`24=3r^3`

Divide 3 on both sides.

`8=r^3`

Cube root on both sides.

`2=r`

The radius of the base is 2 units.

Solve for h.

`24\pi =\pi (2)^2 h`

Cancel
`\pi` on both sides.

`24=4h`

Divide both sides by 4.

`6=h`

Answer 2

6 units

Explanation:

Let, Radius = r units

Height ( h ) = 3r units

Volume ( V ) = 24π units³

Now,

Let's find the height of the cylinder:

`\pi {r}^(2) h \: = 24\pi`

`{r}^(2) (3r) = 24`

Calculate the product

`3 {r}^(3) = 24`

Divide both sides of equation by 3

`\frac{3 {r}^( 3) }{3} = (24)/(3)`

Calculate

`{r}^(3) = 8`

Write the number in the exponential form with an exponent of 3

`{r}^(3) = {2}^(3)`

Take the root of both sides of the equation

`r = 2`

Replacing value,

Height = 3r

`= 3 * 2`

Calculate

`= 6 \: units`

Hope this helps..

Best regards!!