Question

what is the lateral surface area of cuboid cube ?

Answer 1

AnswEr:

If out of the six faces of a cuboid, we only find the sum of the areas of four faces leaving the bottom and top faces. This sum is called the lateral surface area of a cuboid.

๑ Imagine a cuboid of length l, breadth b and height h.

$\star$ $\sf\underline\green{Lateral\:surface\:area\:of\:the\:cuboid}$

= Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC.

$\Rightarrow$ $\sf{2(b\times\:h)+2(l\times\:h)}$

$\Rightarrow$ $\sf{2(l+b)\times\:h}$

$\Rightarrow$ $\sf{2(Length+Breadth)\times\:height}$

$\Rightarrow$ $\sf{Perimeter\:of\:the\:base\times\:Height}$

● Lateral surface area of the cube = $\sf{2(l\times\:l+l\times\:l)}$

= $\sf{2(l^2+l^2=4l^2=4(Edge)^2}$

_____________________________

$\mathfrak\pink{Summary:}$

◕ $\sf{Total\:surface\:area\:of\:a\:cuboid=2(lb+bh+hl)}$

◕ $\sf{Lateral\:surface\:area\:of\:a\:cuboid=2(l+b)h}$

◕ $\sf{Diagonal\:of\:the\:cuboid=}$$\sf\sqrt{l^2+b^2+h^2}$

◕ $\sf{Length\:of\:all\:12\:edges\:of\:a\:cuboid=4(l+b+h)}$

---- If the length of each edges of a cube is l units, then

◕ $\sf{Total\:surface\:area=6l^2}$

◕ $\sf{Lateral\:surface\:area=4l^2}$

◕ $\sf{Diagonal\:of\:the\:cube=}$$\sf\sqrt{3}l$

◕ $\sf{Length\:of\:all\:12\:edges=12\:l}$

#BAL

#Answerwithquality

Answer 2

Answer:

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

Let us discuss the properties of cuboid based 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 as 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 rest 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

Total Surface Area of Cuboid= 2(lb + bh +lh)

Example: If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm. The find its total surface area.

Given, Length, l = 5 cm, Breadth, b = 3 cm and Height, h = 4 cm.

TSA = 2(lb+bh+lh)

TSA = 2(5 x 3 + 3 x 4 + 5 x 4)

TSA = 2(15 + 12 + 20)

TSA = 2(47) = 94 sq.cm.

Lateral surface area of a Cuboid:

The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.

Consider a Cuboid of length, breadth and height to be l, b and h respectively.

Lateral surface area of the cuboid= Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH

=2(b × h) + 2(l × h)

=2h(l + b)

LSA of Cuboid = 2h(l +b)