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?
A. 2 units
B. 4 units
C. 6 units
D. 8 units

Answer 1

Answer:

C. 6 units

Step-by-step explanation:

Let, the radius of the cylinder = r units.

Then, the height of the cylinder = $3\times r$ = $3r$ units.

Also, the volume of the cylinder is 24π cubic units.

Since, we know,

Volume of a cylinder = $\pi r^{2}h$

i.e. $24\pi=\pi r^{2}(3r)$

i.e. $24=3r^{3}$

i.e. $r^{3}=8$

i.e. r= ±2

Since, the radius cannot be negative.

So, the radius is 2 units.

Then, the height of the cylinder = $3\times 2$ = 6 units.

Hence, option C is correct.

Answer 2

By definition, the volume of a cylinder is given by:
 $V = \pi * r ^ 2 * h$
 Where,
 r: cylinder radius
 h: cylinder height
 On the other hand we have:
 The height is 3 times the radius:
 $h = 3r$
 Therefore, rewriting the volume as a function of the height we have:
 $V = \pi * (\frac{h}{3}) ^ 2 * h$
 $V = ( \frac{1}{9} ) \pi * h ^ 3$
 From here, we clear h.
 We have then:
 $h ^ 3 = \frac{9V}{ \pi}$
 $h = \sqrt[3]{\frac{9V}{ \pi}}$
 Substituting values we have:
 $h = \sqrt[3]{\frac{9(24\pi)}{ \pi}}$
 $h = \sqrt[3]{9*24}$
 $h = \sqrt[3]{216}$
 $h = 6$
 Answer:
 the height of the cylinder is:
 C. 6 units