CalissaRelics Posted September 3, 2016 Report Share Posted September 3, 2016 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 Reply Link to post Share on other sites More sharing options...
Vioh Posted September 3, 2016 Report Share Posted September 3, 2016 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 1 Reply Link to post Share on other sites More sharing options...
Vioh Posted September 4, 2016 Report Share Posted September 4, 2016 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. Reply Link to post Share on other sites More sharing options...
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