What will be the volume of cylinder if altitude makes angle of 45 degree with base
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What will be the volume of cylinder if altitude makes angle of 45 degree with base

[From: ] [author: ] [Date: 13-05-04] [Hit: ]
Call this X.Looking at the right triangle created by X and h, how would you describe the angle (theta) betweenX and h?So,......
given that altitude is 20 cm and radius of base is 10 cm.

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Edit: Corrected an error calculating the volume:

Same as as a regular cylinder, except the perpendicular height must be used or use the formula:
V = π r² h sin(θ)
= π * 100 * 20 * sin(45)
= 1000√2 π cm³
≈ 4442.88 cm³

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Draw a sketch of your leaning tower (skewed) cylinder, and draw a height line ( call it h) from the outside of the top skew to the base. Also draw a "center" line inside the cylinder, from the midpoint of the cylinder at the base to the midpoint at the top. Call this X.
Looking at the right triangle created by X and h, how would you describe the angle (theta) between X and h?
X = h / cos (theta)

So, if the Volume of a normal cylinder is
V = (pi) r^2 * h
then the volume of a skewed cylinder is
V = (pi) r^2 * h * sec ( theta)
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