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