Oblique Cylinder

High School

Definition

A cylinder that has two end planes that are parallel to one another. However, unlike a right cylinder, its lateral surface is not perpendicular to these end planes. These end planes (also known as its bases) don't align perfectly on top of one another.

Worked examples

\(\)Base area \( = \pi r^2, \quad V = \pi r^2 h\)

Volume of an oblique cylinder uses the same formula as a right cylinder—base area times height.

\(\)If \( r = 3 \) and \( h = 5, \) then \( V = \pi(3)^2(5) = 45\pi\)

Height is the perpendicular distance between the parallel bases, not the slant length of the side.

Common mistakes

\(V = \pi r^2 \ell\) where \(\ell\) is the slant edge length → \(V = \pi r^2 h\) where \(h\) is perpendicular distance between bases Use the perpendicular height, not the slanted side measurement.
Oblique cylinders have a different volume formula than right cylinders → Both use \(V = \pi r^2 h\); only the lateral surface area formula differs Cavalieri's principle shows oblique and right cylinders with equal base and height have equal volume.
The bases of an oblique cylinder are not parallel → The bases are parallel; they just don't align vertically above each other Parallel planes can be offset horizontally—that tilt defines the oblique cylinder.

Where you'll use it next

Oblique cylinders appear in surface-area and volume problems in geometry and pre-calculus, Cavalieri's principle proofs, and real-world modeling of tilted tubes and pistons in physics and engineering.

Found in 1 StudyPug lesson

Surface area and volume of cylinders

8th Grade Math

A cylinder is like stacking up a pile of circle plates. With information such as, height, radius, and circumference, it is easy to calculate the surface area and volume of cylinders.Let's look at how to calculate the surface area and volume of composite solids too.

8th Grade8th