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 approximate/decimal values and the calculator cannot find a solution, use exact values or rewrite the decimals as fractions.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Find the volume of the solid obtained by rotating the region bounded by the curves $$$y = x^{4}$$$, $$$y = x$$$ about $$$y = 0$$$ using the method of rings.

Solution

$$$\pi \int\limits_{0}^{1} \left(\left(\left(x\right) - \left(0\right)\right)^{2} - \left(\left(x^{4}\right) - \left(0\right)\right)^{2}\right)\, dx = \frac{2 \pi}{9}\approx 0.698131700797732$$$

$$$V = \frac{2 \pi}{9}$$$

Answer

$$$V = \frac{2 \pi}{9}\approx 0.698131700797732$$$A

Volume of Solid of Revolution Calculator

Find volume of solid of revolution step by step

Your Input

Solution

Answer