Wednesday, May 23, 2012

Right Cylinders and Skewed Cylinders

Blog Entry # 103: One of my favorite things to do in mathematics is to find areas and volumes of unusual shapes.

Volume of a Right Cylinder (Figure A)

V = π R^2 H

R = radius
H = height

Volume of a Skewed Cylinder at Angle θ (Figure B)

H resembles the measure from the base to the top of the skewed cylinder. However, to calculate the volume, we will need the length X, not H.

Using trigonometry:

cos θ = H / X

implies that

X = H / (cos θ)

The volume of the skewed cylinder is:

V = π R^2 H sec θ



Until next time, Eddie