Volume of a solid

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§ Problem: Calculate the volume of the solid \( V \), bounded by the given surfaces: \[ V:\left\{\begin{array}{l} x=x^{2}+y^{2} \\ z=x y, \quad z=0 \end{array}\right. \]

9.5.9 Volume of a solid

1.78 $

(3) Problem: Calculate the volume of the solid \( G \), bounded by the given surfaces: \[ \begin{array}{c} G=\left\{(x, y, z): x^{2}+y^{2}-4 x-4 y+z \leq 14\right. \\ \left.z \geq x^{2}+y^{2}\right\} \end{array} \]

9.5.10 Volume of a solid

1.78 $

食 Problem: The center of a moving circular disc moves along the major axis of an ellipse, with the plane of the disc being perpendicular to the plane of the ellipse, and the radius of the circle at each moment being equal to the ordinate of the ellipse. Calculate the volume of the solid that is obtained when the circular disc moves from one vertex to another.

9.5.7 Volume of a solid

1.53 $

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