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We see various objects in our daily lives, such as books, pencil boxes, cones, footballs, and cylinders. All of these things are three-dimensional (solid shapes). All of these objects are three-dimensional and have a shape. There are many forms that have two or more identical (congruent) faces.
Many objects have been noticed in everyday life, including a wooden box, a matchbox, a tea packet, a chalk box, a dice, and a book. All of these objects have the same shape. Six rectangular or square planes make up each of these things. These objects have either a cuboid or a cube shape in mathematics. With the help of their properties and formulas for surface area and volume.The total of all the areas of the shapes that cover the object’s surface is the object’s surface area. If the area of one side is a2, the surface area of six sides is 6a2.
Cube
In the three-dimensional plane, a cube is a 3-dimensional box-like figure. The face of a cube is divided into six equal squares.. At the cube’s vertices, three sides meet. The XYZ plane defines a cube, which is a three-dimensional shape. The cube’s square faces are all the same size and shape.
We know the cube has six square faces. Consider the case where each cube side is a.
The total surface area of the cube = 6a2.
Length of Edge of Cube
By rearranging the formula, we can determine the length of the cube’s edge from its surface area.
Area = 6side2
side2=Area/6
side=√(Area/6)
Examples
What is the Total Surface Area of a cubic structure with a 5m sidewall?
Solution: Given, length of sidewall = 5m
Total surface Area = 6a2
= 6 (52)
= 6 (25)
= 150 m2
If the cube’s area is 294 square metres, what is the length of its edge?
Solution: Given, Area = 294 m2
Length of edge of cube = √(Area/6)
= √(294/6)
= √ 49
= 7 m
Cuboid
A polyhedron with six faces, eight vertices, & twelve edges is referred to as a cuboid. The cuboid’s faces are perpendicular. A cuboid’s faces, however, are not all of the same size.
A cuboid is composed of six rectangular planes with varying lengths, widths, and heights. From the side, it could be a brick or a box with a rectangular view. A cuboid is a solid that has six rectangular faces and is three-dimensional. It has eight edges and twelve vertices. Cuboids always have equal opposite faces.
There are three dimensions to a cuboid. Volume, total surface area, and lateral surface area The area of the surface is measured in square units.
Total Surface Area of a Cuboid
Total Surface Area is equal to the total of a cuboid’s six rectangular sides.
Total Surface Area=2 (l×w+w×h+l×h)
l = length, w = width, h = height
Lateral Surface Area of a Cuboid
A cuboid’s Lateral Surface Area is the total of its four rectangular sides, except its base and top.
Lateral surface Area=2(l×h+w×h)
=2h(l+w)sq.unit
Example:
Find the total surface area of a cuboid with dimensions of 4cm long, 3cm wide, and 2cm high.
Solution:
Given h = 2cm, l = 4cm, w = 3cm
Total Surface Area=2 (l×w+w×h+l×h)
= 2 (4 × 3 + 3× 2 + 2× 4)
= 2 (12 + 6 + 8)
= 2 (26)
= 52 cm2
If the cuboid’s length, breadth, and height are 8cm, 9cm, and 10cm, respectively, what is its Lateral Surface area?
Solution:
Given length = 8cm
breadth = 9cm, height = 10cm
Lateral Surface Area = 2h (l + b)
= 2 × 10 (8 + 9)
= 2 ×10 (17)
= 2 × 170
= 340 cm2
How to identify a cuboid?
Each face of a cuboid is a rectangle, with 90-degree angles at the corners or vertices. Furthermore, the opposite faces have always been the same. A book, for example, is a cuboid. It has six surfaces, some of which are identical to the opposing pair in size.
How to identify a cube?
Six square-shaped sides make up a cube. Cubes also contain eight vertices (corners) and twelve equal-length edges. A cube’s angles are all right angles. Building blocks and dice are examples of cube-shaped objects.
Difference between Cube and Cuboid
The cube’s edges (sides) are all the same length, whereas a cuboid’s edges are all various lengths.
All of the sides of the cube are square, but all of the sides of the cuboid are rectangular.
Only the diagonals of parallel sides of a cuboid are equal, but the diagonals of a cube are all equal.
Conclusion
We observe various items in our daily lives, such as notebooks, matchboxes, instrumental geometry boxes, cones, cricket balls, cylinders, and so on. All of these things are three-dimensional (solid shapes). All of these objects have three dimensions: length, breadth, height, and depth.
Furthermore, we frequently come across shapes that have two or more identical (congruent) faces. The Cube, for example, has squared faces on each side, but the Cuboid has rectangular faces. A three-dimensional form having six faces, eight vertices, and twelve edges is known as a Cube or Cuboid. A cube has the same length, width, and height on all sides, whereas a cuboid has different lengths, widths, and heights. Although both shapes appear to be almost identical, they have distinct qualities.
