Applications of Integration - Volume of Revolution about the y-axis

Applications of Integration - Volume of Revolution about the y-axis

TGM Original Questions

Region \(A\) is bounded by \({{y}^{2}}=4x\), \(y\)-axis and \(y=3-x\).
Region \(B\) is bounded by \({{y}^{2}}=4x\), \(x\)-axis and \(y=3-x\) in the first quadrant.
Region \(C\) is bounded by \({{y}^{2}}=4x\), \(x\)-axis and \(y=3-x\) in the forth quadrant.
Find

  1. volume of \(A\) rotated through \(4\) right angles about \(x\)-axis;

  2. volume of \(B\) rotated through \(4\) right angles about \(y\)-axis;

  3. volume of \(C\) rotated through \(4\) right angles about \(x\)-axis;

  4. volume of total regions of \(A\), \(B\) and \(C\) rotated through \(4\) right angles about \(y\)-axis.

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Answer:(i) \(13.6\) units\(^3\) (ii) \(26.0\) units\(^3\) (iii) \(283\) units\(^3\) (iv) \(458\) units\(^3\)

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