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.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

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

Solution

Answer