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Solution assignment 07 Area and volume

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Assignment 7

Calculate the volume of the cone which is the result of revolving the line y=\displaystyle\frac{1}{2}x, x\in[0,2] around the X-axis.

Solution

We use the formula:

\displaystyle\int_{0}^{2}\pi{y^2}dx=\int_{0}^{2}\pi(\frac{1}{2}x)^2dx=

\displaystyle[\frac{1}{4}.\frac{1}{3}\pi{x^3}]_{0}^{2}=\frac{2}{3}\pi

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