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Volume of Solid of Revolution - Past HSC Exam Question (1 Viewer)

phoenix159

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A bowl is formed by rotating the part of the curve y = x^4 / 4 between x=0 and x=2 about the y axis.
Find the volume of the bowl.

From: 2002 Mathematics Exam (2 Unit)
 

Shazer2

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Pretty sure that might be wrong, but gave it a go.
 
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bottleofyarn

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I found the paper and there's a diagram which clears some ambiguity here (2002 q6c).
This means that you should integrate with respect to y from 0 to 4 since you're rotating about the y axis.
Then, you want the volume between the curve and y=4:

which is simple enough and gives you 32pi/3.

Had a glance at the marking report and the method should be right.
 

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