Cross Sections and Solids of Revolution

A cross section is the intersection of a solid object with a plane, revealing the shape of the object at that particular slice.

The cross section of a cylinder is a circle.

The cross section of a cube can be a square, rectangle, or other shapes depending on the angle of the cut.

A solid of revolution is a three-dimensional shape created by rotating a two-dimensional shape around an axis.

Volume = πr²h, where r is the radius and h is the height.

Volume = (1/3)πr²h, where r is the radius and h is the height.

Volume = (1/3)πh(R² + Rr + r²), where R is the radius of the top base, r is the radius of the bottom base, and h is the height.

A triangular cross section is formed when a plane intersects a solid in such a way that the intersection is a triangle.

To determine the cross section, visualize or draw a plane cutting through the solid and identify the shape formed.

Cross sections can be used to calculate the volume of solids by integrating the area of the cross sections along the height of the solid.