Volume of a solid of revolution

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3) Problem: Calculate the volume of the solid of revolution obtained by the rotation of the figure \( D \) around the axis \( O X \), where \[ D:\left\{\begin{array}{c} y=x+\sin x \\ y=0, \quad x=0, \quad x=\pi \end{array}\right. \]

9.6.1 Volume of a solid of revolution

1.27 $

全 Problem: Calculate the volume of the solid formed by rotating around the axis \( O y \) the figure bounded by the lines: \( \frac{x^{2}}{9}-\frac{y^{2}}{4}=1, x=6 \). Let's plot the drawing.

9.6.2 Volume of a solid of revolution

2.04 $

3) Problem: Calculate the volume of the solid, formed by rotating around the axis \( O x \) of the figure, bounded by the lines: \[ 2 x-y-2=0, y=0, x=3 \] Let's make a drawing.

9.6.4 Volume of a solid of revolution

1.27 $

T Problem: Calculate the volume of the solid formed by rotating around the axis \( O x \) of the figure, bounded by the lines: \( y=x^{2}, y=1 \). Let's plot the drawing.

9.6.3 Volume of a solid of revolution

1.27 $

震 Problem: Calculate the volume of the solid of revolution obtained by the rotation of the figure \( x^{2}+(y-2)^{2}=4 \) around the axis 0X.

9.6.5 Volume of a solid of revolution

1.27 $