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.
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.
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
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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9th Grade Math
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