A right circular cylinder has a height of 20.5 ft and a diameter that is 1.2 times its height.

1. Find the height of the cylinder.

The height of the cylinder is given as 20.5 ft.

2. Find the diameter of the cylinder.

Diameter = 1.2 × height = 1.2 × 20.5 ft

3. Find the radius of the cylinder.

Radius = Diameter / 2

4. Use the formula to find the volume of the cylinder.

Volume = \(\pi \times \text{radius}^2 \times \text{height}\)

Use \(\pi = 3.14\)

5. Round your final answer to the nearest hundredth.

6. Express your answer using the correct unit of measure.

(Optionally, draw a picture on scrap paper to assist with visualization.)

Explain your work or show each step in solving the problem.

The height of the cylinder is 20.5 feet, and the diameter is 1.2 times the height, resulting in a radius of 12.3 feet. The volume of the cylinder, using the formula V =
au r^2 h and 3.14 for
au, is 9695.73 cubic feet when rounded to the nearest hundredth.

Explanation:

The height of the cylinder is given as 20.5 feet. The diameter is 1.2 times the height, therefore:

1.2 imes 20.5 ft = 24.6 ft

Next, the radius, which is half of the diameter:

24.6 ft / 2 = 12.3 ft

Now, we will calculate the volume:

V =
[tex]au r^2 h[/tex]
=[tex]3.14 imes (12.3 ft)^2 imes 20.5 ft[/tex]
= [tex]3.14 imes 151.29 ft^2 imes 20.5 ft[/tex]
=[tex]9695.73 ft^3[/tex]

Finally, rounding the volume to the nearest hundredth:

Volume
V
= [tex]9695.73 ft^3[/tex]