CAT / #Quantitative Ability

October 20, 2017 @ 12:49 PM

October 20, 2017 @ 12:49 PM

K. J. Somaiya Institute of Management Studies and Research, Mumbai

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Cube (Detailed Concept)

Friday, 20th October 2017 12:50 PM​
 
Quantitative Ability – Cube (Detailed Concept)
 
Definition – 
 
A solid with six congruent square faces. A regular hexahedron.
 
A cube is a region of space formed by six identical square faces joined along their edges. Three edges join at each corner to form a vertex. The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids.
 
Parts of a cube – 
 
Face:
 
Also called facets or sides. A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles. 
 
Edge:
 
A line segment formed where two edges meet. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length.
 
Vertex:
 
A point formed where three edges meet. A cube has 8 vertices.
 
Face Diagonals:
 
Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cube.
 
Space Diagonals:
 
Space diagonals are line segments linking the opposite corners of a cube, cutting through its interior. A cube has 4 space diagonals.
 
Volume enclosed by a cube:
 
Definition –
 
The number of cubic units that will exactly fill a cube
 
How to find the volume of a cube?
 
Recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. So if the length of an edge is 4, the volume is 4 x 4 x 4 = 64
 
Or as a formula; Volume = s3 where: S is the length of any edge of the cube.
 
Surface area of a cube:
 
Definition – 
 
The number of square units that will exactly cover the surface of a cube
 
How to find the surface area of a cube
 
Recall that a cube has all edges the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face.
 
Or as a formula; Surface area = 6s2 where:S is the length of any edge of the cube.
 
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