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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

Respuesta :

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:

[tex]\pi {r}^{2} h \: = 24\pi[/tex]

[tex] {r}^{2} (3r) = 24[/tex]

Calculate the product

[tex]3 {r}^{3} = 24[/tex]

Divide both sides of equation by 3

[tex] \frac{3 {r}^{ 3} }{3} = \frac{24}{3} [/tex]

Calculate

[tex] {r}^{3} = 8[/tex]

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

[tex] {r}^{3} = {2}^{3} [/tex]

Take the root of both sides of the equation

[tex]r = 2[/tex]

Replacing value,

Height = 3r

[tex] = 3 \times 2[/tex]

Calculate

[tex] = 6 \: units[/tex]

Hope this helps..

Best regards!!

09pqr4sT

Answer:

[tex]\boxed{6 \: \mathrm{units}}[/tex]

Step-by-step explanation:

The formula for volume of cylinder is:

[tex]V=\pi r^2 h\\V:volume\\r:radius\\h:height[/tex]

[tex]V=24\pi\\h=3r[/tex]

Solve for r.

[tex]24\pi =\pi r^2 (3r)[/tex]

Cancel [tex]\pi[/tex] on both sides.

[tex]24=3r^3[/tex]

Divide 3 on both sides.

[tex]8=r^3[/tex]

Cube root on both sides.

[tex]2=r[/tex]

The radius of the base is 2 units.

Solve for h.

[tex]24\pi =\pi (2)^2 h[/tex]

Cancel [tex]\pi[/tex] on both sides.

[tex]24=4h[/tex]

Divide both sides by 4.

[tex]6=h[/tex]

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