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Sam will pour 3 gallons of water into a cylindrical container. After he pours all the water into the cylindrical container, it will be 90% full. If the diameter of the container is 8 inches, what is the approximate height of the container in inches?
For water, use the conversion 1 cubic foot = 7.48 gallons

a. 14.16
b. 1.29
c. 116.16
d. 15.48

Sagot :

Using the volume of a cylinder, it is found that the approximate height of the container in inches is given by:

d. 15.48

What is the volume of a cylinder?

The volume of a cylinder of radius r and height h is given by:

[tex]V = \pi r^2h[/tex]

In this problem, Sam pours 3 gallons of water into a cylindrical container, and it will be 90% full. Hence, the volume, in cubic feet, is:

[tex]0.9V = \frac{3}{7.48}[/tex]

[tex]V = \frac{3}{0.9(7.48)}[/tex]

[tex]V = 0.4456[/tex]

The diameter of the container is 8 inches, hence the radius is of 4 inches = 0.3333 feet, considering a feet has 12 inches.

The height, in feet, will be given by:

[tex]V = \pi r^2h[/tex]

[tex]0.4456 = (0.3333)^2\pih[/tex]

[tex]h = \frac{0.4456}{(0.3333)^2\pi}[/tex]

[tex]h = 1.2768[/tex]

Considering a feet has 12 inches, in inches, the height will be of:

1.2768 x 12 = 15.48

Hence option D is correct.

You can learn more about the volume of a cylinder at https://brainly.com/question/9408912

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