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Volume of Revolution!


CalissaRelics

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How can we solve this problem?????

An open glass is created by rotating the curve y = x2, defined in the domain x [0, 10], 
2π radians about the y-axis. Units on the coordinate axes are defined to be in centimetres. 

(a) When the glass contains water to a height h cm, find the volume V of water in terms of h. 

Thanks

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The screenshot attached is my solution for this question. The final answer I got is pi*h^2/2 (where h must not be bigger that 10^2=100 since the domain of x is [0,10]). If anyone spots any mistakes in my working, please do tell. It has been a while since I last touched calculus :P

Untitled.png

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As suggested by @kw0573, we can actually solve this question using a much simpler method (see below). For this particular question, integrating using dy is much easier than using dx, because y=x^2 (which is exactly what appears inside the integral) and we don't even have to convert the limits.

Untitled.png

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