Dynamic Calculus

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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?
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  1. 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.
  2. 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.
  3. Check your answer to question (2) using calculus.
  4. 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.
  5. Check your answer to question (4) using calculus. Click the 'checkbox' to confirm your answer.