Rectangular Objects

Rectangular objects are one of the basis of mathematics. Rectangular objects are having six sides. One of the rectangular objects is cuboid. Cuboid are also having six sides. These rectangular cuboid are having same faces like the rectangular objects. Rectangular prism is also included in the rectangular objects. Length of the rectangular prism is equal to the length of the rectangular.

Explanation for rectangular objects

There are many rectangular objects are present. They are defined as,

1. Rectangular cuboid

2.Rectangular prism

Rectangular cuboid:

The volume of the rectangular cuboid are find using the formula that are shown below,

Volume = Height `xx` Width `xx` Length

This can also be written as,

V = h `xx` w `xx` l.

Surface area of the rectangular cuboid are find using the formula,

Surface area = 2wl `xx` 2lh `xx` 2hw

The diagrammatic representation of the cuboid are shown below,



Example problem for rectangular objects

Example problem 1: Find the surface area and volume of the cuboid by using the formula, where the height = 4, length = 3, width = 2.

Solution:

Step 1: The volume of the rectangular cuboid are,

Volume = Height `xx` Width `xx` Length

from given h= 4, l =3, w =2

Step 2: Therefore by substituting the given information, we get,

V = 4 `xx` 3 `xx` 2

= 24.

Therefore, the volume of the cuboid is 24units.

Step 3: The surface area of the cuboid is given by,

Surface area = 2wl `xx` 2lh `xx` 2hw

Step 4: by substituting the above information given, we get,

Surface area = 2 ( 3 `xx` 2 ) `xx` 2( 4 `xx` 3 ) `xx` 2 ( 3 `xx` 2 )

= 2(6) `xx` 2(12) `xx` 2(6)

= 12 `xx` 24 `xx` 12

= 3456

This is the required area for cuboid.

Example problem 2: Find the surface area and volume of the cuboid by using the formula, where the height = 3, length = 4, width = 5.

Solution:

Step 1: The volume of the rectangular cuboid are,

Volume = Height `xx` Width `xx` Length

from given h= 3, l =4, w =5

Step 2: Therefore by substituting the given information, we get,

V = 3 `xx` 4 `xx` 5

= 60

Therefore, the volume of the cuboid is 60 units.

Step 3: The surface area of the cuboid is given by,

Surface area = 2wl `xx` 2lh `xx` 2hw

Step 4: by substituting the above information given, we get,

Surface area = 2 ( 6 `xx` 4 ) `xx` 2( 4 `xx` 3 ) `xx` 2 ( 3 `xx` 6 )

= 2( 24 ) `xx` 2( 12 ) `xx` 2( 18 )

= 288 `xx` 24 `xx` 36

= 248832

This is the required area for cuboid.