Tutorial Week 6

Volumes using Cross-Sectional Areas

Q1: Find the volume of a pyramid-like shape with a square base of side length 4 and height 6. The sides of the pyramid are defined by the function \(y = \frac{6(x-2)^2}{4}\), with the origin of the function being the centre of the pyramid and the x axis running parallel to the sides of the pyramid.

Volumes of Revolution

Q2: Find the volume created by rotating the region bounded between \(y =3-x^{2}\) and \(y =2x^{2}\) on the interval \(x\in[0, 1]\) about the x-axis.

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Volumes by Cylindrical Shells

Q3: Find the volume created by rotating the region bounded below by \(y = 2^x\) and bounded above by \(y = 8\) on \(x \in [0, 3]\) about the y-axis.

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