Volume of solids of revolution - Circle Q (1 Viewer)

gamja

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a) Sketch a graph of the circle (x-3)^2 + y^2 = 1. [straightforward]

b) The region inside the circle is rotated about the y-axis. Show that the volume of the solid formed is given by (x-3)^2 + y^2 = 1 and evaluate the integral.
[I'm not sure what it means by ' Show that the volume of the solid formed is given by (x-3)^2 + y^2 = 1'; and also how to solve volume integral by subtraction if inner area isn't a nice function]
 

nathanzhou1234

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Hmm i think this might be old syllabus stuff not sure if they expect you to calculate non centred circles for volume of solids of rev. I think its gonna be a donut (torus) so there might be a mathematical formula.

go shore
 

Drongoski

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What's given answer of the volume of the torus so-formed?
 

nathanzhou1234

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What's given answer of the volume of the torus so-formed?
the volume of a torus is ((pi)r^2)(2(pi)r). Just not sure if you're allowed to use it. I know that if vol. of solids of resolution gives u a sphere or a cone or stuff ur allowed to use formulas then but not sure about this.
 

5uckerberg

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a) Sketch a graph of the circle (x-3)^2 + y^2 = 1. [straightforward]

b) The region inside the circle is rotated about the y-axis. Show that the volume of the solid formed is given by (x-3)^2 + y^2 = 1 and evaluate the integral.
[I'm not sure what it means by ' Show that the volume of the solid formed is given by (x-3)^2 + y^2 = 1'; and also how to solve volume integral by subtraction if inner area isn't a nice function]
With part b is the volume just a donut and from memory the volume is simply a circle multiplied by the dough formed by the circumference of the circle being rotated around the y-axis.
 

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