A cylinder has a height of #4# feet and a diameter of #12# inches. What is the volume of the cylinder?

1 Answer
Aug 7, 2016

Before calculating the volume of this cylinder, we must either convert the diameter to feet or the height to inches. I'll do the latter, to avoid getting a very small number.

Recall that there are #12# inches in #1# foot. Thus, we can state:

#(12" in.")/(1" ft.") =(x)/(4" ft."#

#x = (12" in." xx 4cancel" ft.")/(1cancel"(ft.)")#

#x = 48" in."#

Hence, the cylinder has a height of #48# inches.

Now, we can apply the formula for volume of a cylinder to effectuate our calculation. The formula in question is #V = a_"base" xx h#, or #V = r^2pi xx h#.

However, we know our diameter but we don't know our radius. As you probably know, the diameter is linked to the radius b the formula #d = 2r#. Solving for #r# and substituting:

#r = d/2#

#r = 12/2#

#r = 6#

#:.# The radius of the cylinder measures #6# inches.

#V = r^2pi xx h#

#V = 6^2pi xx 48#

#V = (36 xx 48)pi#

#V = 1728pi" in"^2#

Note that this answer is in exact value. Rounded to two decimal places, the volume is #5428.67" in"^2#.

Practice exercises:

  1. Determine the volume of a cylinder whose base has a circumference of #18pi" yd."# and whose height measures #27" ft."#.

Note:

•The formula for circumference of a circle is #C = dpi#, where #C# is the circumference.

•There are #3# feet in a yard.

Challenge Problem:

The volume of an industrial sized water cistern is # 200pi" ft"^2#. The height measures #3# feet more than the radius. Determine algebraically the circumference of the base of the cistern, using the formula given above.

Hopefully this helps, and good luck!