1.
85 cm
EXERCISE 13.9 (Optional)*
A wooden bookshelf has external dimensions as
follows: Height
= 110 cm, Depth = 25 cm,
Breadth=85 cm (see Fig. 13.31). The thickness of
the plank is 5 cm everywhere. The external faces
are to be polished and the inner faces are to be
painted. If the rate of polishing is 20 paise per
cm and the rate of painting is 10 paise per cm²,
find the total expenses required for polishing and
painting the surface of the bookshelf.
25
Answers
Definition of Cube and Cuboid
Cube: A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.
Cuboid: A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions.
Difference Between Cube and Cuboid
The sides of the cube are equal but for cuboid they are different.
The sides of the cube are square in shape but for cuboid, they are in a rectangular shape.
All the diagonals of the cube are equal but a cuboid has equal diagonals for only parallel sides.
Learn more differences between cube and cuboid here.
Shape of Cube and Cuboid
As we already know both cube and cuboid are in 3D shape, whose axes goes along the x-axis, y-axis and z-axis plane. Now let us learn in detail.
A cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions.
Cuboid Shape
Properties of a Cuboid
Below are the properties of cuboid, its faces, base and lateral faces, edges and vertices.
Faces of Cuboid
A Cuboid is made up of six rectangles, each of the rectangles is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6 faces of cuboid.
The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces. Any two faces other than the opposite faces are called adjacent faces.
Consider a face ABCD, the adjacent face to this are ABFE, BCGF, CDHG, and ADHE.
Base and lateral faces
Any face of a cuboid may be called the base of the cuboid. The four faces which are adjacent to the base are called the lateral faces of the cuboid. Usually, the surface on which a solid rests on is known to be the base of the solid.
In Figure (1) above, EFGH represents the base of a cuboid.
Edges
The edge of the cuboid is a line segment between any two adjacent vertices.
There are 12 edges, they are AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF and CD and the opposite sides of a rectangle are equal.
Hence, AB=CD=GH=EF, AE=DH=BF=CG and EH=FG=AD=BC.
Vertices of Cuboid
The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid.
A cuboid has 8 vertices A, B, C, D, E, F, G and H represents vertices of the cuboid in fig 1.
By observation, the twelve edges of a cuboid can be grouped into three groups, such that all edges in one group are equal in length, so there are three distinct groups and the groups are named as length, breadth and height.
A solid having its length, breadth, height all to be equal in measurement is called a cube. A cube is a solid bounded by six square plane regions, where the side of the cube is called edge.
Properties of Cube
A cube has six faces and twelve edges of equal length.
It has square-shaped faces.
The angles of the cube in the plane are at a right angle.
Each face of the cube meets four other faces.
Each vertex of the cube meets three faces and three edges.
Opposite edges of the cube are parallel to each other.
Cube and Cuboid Formulas
The formulas for cube and cuboid are defined based on their surface areas, lateral surface areas and volume.
Cube Cuboid
Total Surface Area = 6(side)2 Total Surface area = 2 (Length x Breadth+breadth x height + Length x height)
Lateral Surface Area = 4 (Side)2 Lateral Surface area = 2 height(length + breadth)
Volume of cube = (Side)3 Volume of the cuboid = (length × breadth × height)
Diagonal of a cube = √3l Diagonal of the cuboid =√( l2 + b2 +h2)
Perimeter of cube = 12 x side Perimetr of cuboid = 4 (length + breadth + height)
Surface Area of Cube and Cuboid
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.
Surface area formula of a cuboid
Consider a cuboid having the length to be ‘l’ cm, breadth be ‘b’ cm and height be ‘h’ cm.
Area of face EFGH = Area of Face ABCD = (l× b) cm2
Area of face BFGC = Area of face AEHD = (b ×h) cm2
Area of face DHGC = Area of face ABFE = (l ×h) cm2
Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces