Question

a cylinder has a diameter of 6 feet. the volume of the cylinder is 36/5π cubic feet.

enter the height, in feet, of the cylinder in decimal from. round your answer to the nearest tenth.

Answer 1

Answer:

Height of cylinder is $\frac{4}{5}\ ft$.

Step-by-step explanation:

Diameter of cylinder, D = 6 feet

Relation between Radius, R and diameter, D is given by:

$R = \dfrac{D}{2}$

So, radius, R = $\frac{6}{2} \Rightarrow 3$ feet

Let height of cylinder be $h$ feet.

Formula for volume of cylinder is given by:

$V = \pi R^{2} H$

Where, R is the radius of base of cylinder

and H is the height of cylinder

We are given that,

$V = \dfrac{36 \pi}{5} ft^{3}$

Using formula for volume, $V = \pi R^{2} H$

$\dfrac{36\pi}{5} = \pi \times 3^{2} \times h\\\Rightarrow \dfrac{36\pi}{5} = \pi \times 9 \times h\\\Rightarrow h = \dfrac{4}{5} ft$

Hence, Height of cylinder is $\frac{4}{5}\ ft$.