Surface of revolution 1

Calculus Level 3

Calculate the volume of the surface of revolution obtained by rotating the parabola $y^2 = x$ around the $x$ -axis between $x = 0$ and $x = 2$ .

Submit your answer to 2 decimal places.

$y^2 =x$

The answer is 6.28.

1 solution

Otto Bretscher
Apr 2, 2016

As was known to Archimedes, the volume of a paraboloid is half the volume of the circumscribed cylinder. Thus the answer is $\frac{1}{2}\times 2\pi \times 2=2\pi\approx \boxed{6.28}$ .

Hum, very interesting, I didn't know Archimedes's. I'll study this. As usual, thank you very much, Otto, (+1) $\uparrow$

Guillermo Templado - 5 years, 2 months ago

Surface of revolution 1

The answer is 6.28.

1 solution

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