Cross Section

The cross section of a solid is a plane section resulting from a cut (real or imaginary) perpendicular to the length (or breadth of height) of the solid.

If the shape and size of the cross section is the same at every point along the length (or breadth or height) of the solid then the cross section is uniform.

$Cross Section Perpendicular to Height$

$Cross Section Perpendicular to Length$

The two solids shown above have uniform cross sections.

The figure given below is a solid (Cone) whose cross sections perpendicular to height are not uniform.

$Cross Section of Cone Perpendicular to Height$

Volume of a solid figure with uniform cross section

= (Area of the cross section) × length (or height or breadth)

= A × h

Lateral surface area of a solid figure with uniform cross section

= (Perimeter of the cross section) × length (or height or breadth)

= P × h

$Cross Section of Sold Figure$

Total surface area of a solid figure with uniform cross section

= Lateral surface area + Sum of the areas of the two plane ends

= P × h + 2 × A

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