A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which students have to choose the value that most closely estimates the volume of a cylinder, given its radius, how tall it is (its height), and a value to use for π.
According to the problem, the cylinder is 6 inches tall and has a radius of 3 inches. We have a formula sheet that tells us the formula to use for the volume of a cylinder:
where r is the radius and h the height of a right cylinder. Plugging in the values, we get the answer of
Our answer choices are 36, 54, 113, and 170 cubic inches, of which 170 is the closest to our estimate of 169.56. I say “estimate” because 3.14 is not the exact value of π.
Although this problem seems straightforward (plug-n-chug with the formula), there are some things to watch out for. The biggest cause of error in these problems is when you forget that the radius and the height of the cylinder have to be given to you in the same units. Convert if necessary. Then, the computed volume will be in those cubic units.
Second, some textbooks make a big deal out of saying “the volume enclosed by the cylinder.” This is more mathematically precise, since a cylinder, by strict definition, is the shell of the figure and that shell has, in theory, a thickness of zero. These textbooks aren’t saying something wrong, but neither is your teacher who says “the volume of a cylinder.” One is more “precise” on a higher level of mathematical dialog, but we all know what both people mean. Don’t sweat the small stuff.
And finally, if you would like more practice on cylinder volume problems, visit our online library at VoxLearn.org and search for “cylinder volume.”