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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.

I'll use geometry instead of calculus.

Here's the bucket (turned up-side down):
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".
The top part of the cone is a smaller cone of radius 4.5" and height 7tanθ = 18".

volume of a cone = ⅓πr²h
volume of bucket = (volume of large cone) - (volume of small cone)
= ⅓π7²·28 - ⅓π4.5²·18
≅ 1436.76 - 381.70
= 1055.06 in³

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