Volume of Solid of Revolution Calculator

The calculator will try to find the volume of a solid of revolution using either the method of rings or the method of cylinders/shells, with steps shown.

Curves:

Comma-separated. x-axis is $$$y = 0$$$, y-axis is $$$x = 0$$$.

Lower limit:

Optional.

Upper limit:

Optional.

Rotate about:

x-axis is $$$y = 0$$$, y-axis is $$$x = 0$$$.

Method:

If you are using periodic functions and the calculator cannot find a solution, try to specify the limits. If you don't know the exact limits, specify wider limits that contain the region (see example). Use the graphing calculator to determine the limits.

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Your Input

Find the volume of the solid obtained by rotating the region bounded by the curves $$$y = \sqrt{x}$$$, $$$y = x^{2}$$$ about $$$y = 0$$$ using the method of rings.

Solution

$$$\pi \int\limits_{0}^{1} \left(\left(\left(\sqrt{x}\right) - \left(0\right)\right)^{2} - \left(\left(x^{2}\right) - \left(0\right)\right)^{2}\right)\, dx = \frac{3 \pi}{10}\approx 0.942477796076938$$$

Total volume: $$$V = \frac{3 \pi}{10}$$$.

Answer

Total volume: $$$V = \frac{3 \pi}{10}\approx 0.942477796076938$$$A.

Volume of Solid of Revolution Calculator

Find volume of solid of revolution step by step

Your Input

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