Dynamic Calculus
Home > Integral calculus
The volume of a solid of revolution (x-axis)
What is the volume of the solid of revolution generated when the area bounded by \(y = \frac{x}{4}\), the \(x\)-axis and the ordinates \(x = a\) and \(x = b\) is rotated about the \(x\)-axis?
[You can reset the applet at any time by clicking the 'circular arrows' icon in the top right corner]
- Move the point \(A\) to the origin. Using the area of a triangle formula, calculate the area bounded by the curve, the \(x\)-axis and the ordinates \(x = a\) and \(x = b\). Confirm your answer using calculus.
- Rotate the region in question (1) about the \(x\)-axis by moving the 'slider' to the right. What solid is formed? Without using calculus, calculate the volume of the solid.
- Check your answer to question (2) using calculus.
- Move the point \(A\) to position \((1, 0)\). Again, without using calculus, calculate the volume of the truncated cone formed by rotating the region about the \(x\)-axis.
- Check your answer to question (4) using calculus. Click the 'checkbox' to confirm your answer.