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Calculating the volume of a restaurant take-away box that is circular on the bottom and square on the top

Having a bit of a problem calculating the volume of a take-away box:

enter image description here

I originally wanted to use integration to measure it by rotating around the x-axiz, but realised that when folded the top becomes a square, and the whole thing becomes rather irregular. Since it differs in circumference I won't be able to measure it like I planned.

Is there any method or formula that can be used to measure a shape like this, or do I just have to approximate a cylinder and approximate a box and add those two together?



from Hot Weekly Questions - Mathematics Stack Exchange

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