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

Answer:

6 units

Step-by-step 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

$\frac{3 {r}^{ 3} }{3} = \frac{24}{3}$

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

$= 3 \times 2$

Calculate

$= 6 \: units$

Hope this helps..

Best regards!!

Answer 2

Answer:

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

Step-by-step 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.

$6=h$