Math CentralQuandaries & Queries


Question from Jackie:

Rectangular prism that is 40 by 20 with rounded corners with a radius of 2.5.

What would the surface area be?

Hi Jackie,

You didn't supply units and also the dimensions of a rectangular prism are the length and width as well as the height. You only supplied two measurements so I can't complete your problem but let me describe a way to approach it.

In the Physics Forums site there is a similar question asking for the volume of a cube with rounded corners. A solution is described which removes a small cube of side length $s$ from each corner and replacing it by one-eighth of a sphere of radius $s.$ Can you see how to apply the same method to calculating the surface area?


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