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

[gamja]

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]

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]

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

 

[nathanzhou1234]

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]

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.