Determine Volume of Mug
How much coffee does the mug shown at the right hold?
Given:
Inside Diameter = 2.50”
Overall height of the mug = 3.75”
Thickness of the bottom = 0.25”
Coffee cups are not filled to the brim. Allow 0.5” space at
the top.
![](data:image/png;base64,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)
Answer:
Volume of a cylinder = π * Radius2 * Height
“Height” of coffee = 3.75” - 0.25” - 0.5” = 3.0”
Radius = Diameter ÷ 2
Volume = 3.14 * 1.252 * 3.0 = 14.72 in3
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How much coffee does the mug shown at the right hold?
Given:
Inside Diameter = 2.50”
Overall height of the mug = 3.75”
Thickness of the bottom = 0.25”
Coffee cups are not filled to the brim. Allow 0.5” space at
the top.
Answer:
Volume of a cylinder = π * Radius2 * Height
“Height” of coffee = 3.75” - 0.25” - 0.5” = 3.0”
Radius = Diameter ÷ 2
Volume = 3.14 * 1.252 * 3.0 = 14.72 in3
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