Volume of Solid of Revolution Calculator
Find volume of solid of revolution step by step
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.
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.