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RD Sharma Class 8 Solutions Chapter 21 – Volumes Surface Area Cuboid Cube (Ex 21.3) Exercise 21.3

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RD Sharma Class 8 Solutions Chapter 21 – Volumes Surface Area Cuboid Cube (Ex 21.3) Exercise 21.3 – Free PDF

Free PDF download of RD Sharma Class 8 Solutions Chapter 21 –- Volumes Surface Area Cuboid Cube Exercise 21.3 solved by Expert Mathematics Teachers on Vedantu. All Chapter 21 –- Volumes Surface Area Cuboid Cube Ex 21.3 Questions with Solutions for RD Sharma Class 8 Maths to help you to revise the complete Syllabus and sScore mMore marks. 


Unlike previous exercises, here, we will see how to find the surface area of a cube and cuboid. Moreover, we will also look at how the surface area of four walls is calculated. This is what exercise 21.3 is all about. The PDF provided here on Vedantu is free and you can have a look at it whenever you get stuck on the question or if you want to see how a particular question is solved. Vedantu has got your back and will help you throughout the journey of your study. 

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Cuboids and Cubes

Three-dimensional shapes with six faces, eight vertices, and twelve edges are known as cubes and cuboids. The main distinction is that a cube has the same length, width, and height on all sides, whereas a cuboid has varied length, breadth, and height. Both shapes appear to be nearly the same, however, they have different qualities. Both the cube and the cuboid have different areas and different volumes.


Many objects, such as a box, a packet, a chalk box, a dice, a book, and so on, are encountered in everyday life. All of these items have the same form. All of these items are made up of six rectangular or square planes. These objects have the shape of a cuboid or a cube in mathematics. We'll learn the surface area and volume formulas here.

A Cuboid and A Cube's Surface Area

We saw in section 21.2 that a cuboid's surface is made up of six rectangular faces. As a result, a cuboid's surface area is equal to the sum of the areas of its six rectangular sides. Let's look at the formula for a cuboid's surface area. 


NOTE: The length, breadth, and height of a cuboid must all be given in the same units for calculating its surface area. 


The Cube's Surface Area 

We have l = b = h for a cube since all six faces are squares of the same size.


The Walls of the Room’s Surface Area

We learned the formula for the surface area of a cuboid and a cube in the previous lesson. We'll get a formula for the surface area of a room's walls in this section. Consider a room with measurements of lcm, b cm, and h cm for length, width, and height, respectively. A room has four walls, two long and two short in rectangle shape each. Each long wall measures l cm by h cm, while each short wall is b cm by h cm.


Surface area of the four walls =  {2 (l x h) + 2 (b x h)} cm²                                                   

                                                       = 2 x (Length + Breadth) x Height

                                                       = (Perimeter of the floor) x Height

                                                         ∴2 (l+b) x h


Links to Other Exercises of Chapter 21

Class 8 Maths Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.1

Class 8 Maths Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.2

Class 8 Maths Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.3

Class 8 Maths Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.4

 

Cubes and Cuboids Formulas


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 = \[\sqrt{3}\] x side

Diagonal of the cuboid = l2+b2+h2

Perimeter of cube = 12 x side

Perimeter of cuboid = 4 (length + breadth + height)


Lateral Surface Area

The lateral surface area of a cuboid is equal to the total of the areas of its four side faces, except the bottom and top faces. The sum of the area of a room's four walls is an example of lateral surface area. The formula for calculating a cuboid's lateral surface area is


Area of four sides = 2 (l × h) + 2 (b × h) = 2 (l + b) h = perimeter of base × height

Alternatively,


A cuboid's lateral surface area = 2(l+b)h


Vedantu offers RD Sharma Solutions for Class 8 Chapter 21 to help students ace their exams. These solutions are easily available online and can be downloaded in PDF format for free. 

FAQs on RD Sharma Class 8 Solutions Chapter 21 – Volumes Surface Area Cuboid Cube (Ex 21.3) Exercise 21.3

1. How do we define cube and cuboid differently?

In mathematics, the cube and cuboid are three-dimensional shapes. Rotating two-dimensional geometries known as square and rectangle, respectively, form the cube and cuboid.


Cube: A cube is a three-dimensional shape with the XYZ plane as its definition. This object has six faces, eight vertices, and twelve edges. All of the cube's faces are square and have the same measurements.


Cuboid: A cuboid is a polyhedron having six faces, eight vertices, and twelve edges. The cuboid's faces are parallel. A cuboid's faces, on the other hand, are not all the same size.


For more such information students can go to the Vedantu app or the Vedantu website and learn more about the concepts in detail. Vedantu provides free access to all the explanations and study material which will help students learn in a hassle-free way.

2. What are some properties of a cube?

A cube has numerous properties if somebody has to count. Since the question has been asked, here are the properties of the cube listed below.

  • There are a total of six faces and twelve edges of equal length in a cube.

  • Square-shaped faces form a cube.

  • In the plane, the angles of the cube are at a right angle.

  • Four other faces are always met by each face of a cube.

  • Three faces and three edges meet each vertex of the cube.

  • The cube's opposite edges are parallel to one other.

3. What is the difference between the lateral surface area of the cube and the total surface area of the cube?

The difference between the lateral surface area of the cube and the total surface area of the cube is as follows:


Cube's total surface area: A cube's total surface area refers to the total area covered by all six of its faces. The sum of the areas of these 6 faces is used to calculate TSA.


Cube's lateral surface area: The total area covered by a cube's side or lateral face is referred to as the lateral surface area. The sum of the areas of these four faces is used to determine LSA.