Most tests often include questions based on the knowledge of the geometries of 3-D objects such as cylinder, cone, cuboid, cube & sphere. The purpose of the article is to help you learn basics of 3-D geometry and encapsulate some of the important formulae and tricks.
The questions on Volume and Surface Area appear in all the competitive exams. Most of the students tend to avoid this topic considering it to be quite complex and calculative. This article would help you not only in memorizing the formulas, but also in understanding direct or indirect applications of these formulas. We strongly advice you go through each and every definition and formula given below to solve questions on Surface Area and Volume.
Surface area and Volume Formulas
Solids: Solids are three–dimensional objects, bound by one or more surfaces. Plane surfaces of a solid are called its faces. The lines of intersection of adjacent faces are called edges.
For any regular solid, Number of faces + Number of vertices = Number of edges + 2. This formula is called Euler’s formula.
Volume: Volume of a solid figure is the amount of space enclosed by its bounding surfaces. Volume is measured in cubic units.
A prism is a solid, whose vertical faces are rectangular and whose bases are parallel polygons of equal area. A prism is said to be triangular prism, pentagonal prism, hexagonal prism, octagonal prism according to number of sides of the polygon that form the base. In a prism with a base of n sides, number of vertices = 2n, number of faces = n + 2.
Surface area formula of vertical faces of a prism = perimeter of base x height.
Total surface area of a prism = perimeter of base x height + 2 x area of base
Volume of a prism = area of base x height