Advanced Math/Volume

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Question
A tin pail has the following dimensions:

Top- 14 inches in diameter

Bottom- 9 inches in diameter

Height- 10 inches

Calculate volume (in quarts) of the pail.  Thank you.

Answer
I'll use geometry instead of calculus.

Here's the bucket (turned up-side down):
https://www.flickr.com/photos/dwread/14519367362/
Let θ be the slant angle of the side.
tanθ = 10/2.5 = 4

The bucket is the bottom part of a cone of radius 7" and height 7tanθ = 28".
https://www.flickr.com/photos/dwread/14519367412/
The top part of the cone is a smaller cone of radius 4.5" and height 7tanθ = 18".

volume of a cone = ⅓πrh
volume of bucket = (volume of large cone) - (volume of small cone)
= ⅓π728 - ⅓π4.518
≅ 1436.76 - 381.70
= 1055.06 in

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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