Long description: block2fig2

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The image displays a graph with a line segment forming a cone and an ellipse formed by revolving the line \(y=2x\) around the x-axis.

Alt text: A graph shows a line segment forming a cone and an ellipse formed by revolving the line \(y=2x\) around the x-axis.

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  • The image displays a two-dimensional Cartesian coordinate system with the horizontal axis labeled \(x\) and the vertical axis labeled \(y\), both marked with numerical tick lines.
  • A straight line passes through the origin and has the equation \(y=2x\).
  • The area bounded by the line \(y=2x\), the \(x\)-axis, and vertical lines at \(x=0\) and \(x=3\) is shaded to form a triangle, which represents a cone when revolved around the \(x\)-axis.
  • Overlapping the area of the triangle is an ellipse, which is the solid generated by revolving the line \(y=2x\) around the \(x\)-axis for \(x\) values from \(0\) to \(3\).

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