Mechanical and Materials Engineering Homework Solutions
Problem
#2010

Volume Using Multiple Integration

This is a PAST exam question.
Please help me understand how to go about questions a and b.

I think I need some kind of double integral or something?

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Engineering_B.doc
Systems Engineering B

The shape of the hull of a small barge of width w, length l and depth d,
can be approximated by the multivariable function f(x,y), where:



(a) Show via multiple integration that the volume V of the hull is
given by the following expression:



(b) If the mass of the barge is 100 tonnes, and its sides must clear
the water by at least 1 m to safeguard against sinking, what is the
maximum payload of the vessel, to the nearest 100 tonnes?

Vessel dimensions: w=6m

l=20m

d=9m
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