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Volume by Shell Method Calculator
Find the volume of a solid of revolution about the y axis using cylindrical shells for f(x) = ax2 + bx + c.
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Find the volume of a solid of revolution about the y axis using cylindrical shells for f(x) = ax2 + bx + c.
Volume by Shell Method Estimator
Enter your numbers below for an instant estimate.
0
π‘ Tip: V = 2 pi x integral of x f(x) dx from a to b.
How It Works
Key concepts behind this calculator
1
Enter Values
Fill in each field with your own numbers.
2
Calculate
Results update as you change the inputs.
3
Review
Read the breakdown and the explanation.
4
Adjust
Change values to compare scenarios.
Quick Reference Guide
Volume Quick Guide
Typical values for reference.
| f(x) | Limits | Spare | Volume |
|---|---|---|---|
| 1xΒ² | 0 to 1 | – | 1.5708 |
| 1xΒ² | 0 to 2 | – | 25.1327 |
| 1x | 0 to 3 | – | 56.5487 |
| 2 | 1 to 3 | – | 50.2655 |
| Rule of Thumb | Check inputs | Use as a guide | Round sensibly |
Common Questions
Volume by Shell Calculator FAQ
Answers to common questions about this calculator.
Summing thin cylindrical shells of radius x and height f(x).
When rotating about the y axis with f given in terms of x.
V = 2 pi times the integral of x f(x).
Use non-negative limits.