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Question

A rectangular box having length, breadth and height as (a+b+c),(a2+b2) and (2a+2b+2c) respectively. Find the volume of the box.  [4 MARKS]


Solution

Concept: 1 Mark
Application: 3 Marks

Total volume =

(a+b+c)(a2+b2)(2a+2b+2c)

=(a3+ab2+a2b+b3+ca2+cb2)(2a+2b+2c)

=(2a4+2a3b+2a3c+2a2b2+2ab3+2ab2c+2a3b+2a2b2+2a2bc+2ab3+2b4+2b3c+2a3c+2a2bc+2a2c2+2ab2c+2b3c+2b2c2)

=(2a4+4a3b+4a3c+4a2b2+4ab3+4ab2c+4a2bc+2b4+4b3c+2a2c2+2b2c2)

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