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RD Sharma Solutions

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

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.

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. What is the correct method to calculate the volume of a cuboid for Class 8 Maths problems?

To solve for the volume of a cuboid, you must use the formula Volume = length × breadth × height. First, identify the values for length (l), breadth (b), and height (h) from the problem. Ensure all dimensions are in the same unit. Then, multiply these three values together. The final answer should be expressed in cubic units, such as cm³ or m³.

2. How do you find the Total Surface Area (TSA) of a cuboid as per the method in RD Sharma solutions?

The step-by-step method to find the Total Surface Area (TSA) of a cuboid is to use the formula: TSA = 2 × (lb + bh + hl). This formula accounts for the area of all six rectangular faces of the cuboid. You need to calculate the area of the three unique pairs of faces (top and bottom, front and back, left and right sides) and then sum them up. The final answer is always in square units (e.g., cm²).

3. What is the difference between finding the Lateral Surface Area (LSA) and Total Surface Area (TSA) of a cube?

The key difference lies in which faces are included in the calculation.

The Total Surface Area (TSA) includes the area of all six faces of the cube, calculated using the formula TSA = 6a², where 'a' is the side length.
The Lateral Surface Area (LSA) includes the area of only the four vertical faces (the 'walls'), excluding the top and bottom faces. It is calculated using the formula LSA = 4a².

For problem-solving, you use LSA when dealing with the area of the four walls of a room, and TSA for the entire surface of a closed box.

4. Why is the unit for the volume of a cuboid 'cubic units' (e.g., m³) while its surface area is in 'square units' (e.g., m²)?

This is because area and volume measure fundamentally different properties.

Surface Area is a two-dimensional measurement. It measures the total flat space covering the object's exterior, which involves multiplying two dimensions at a time (like length × breadth). This results in square units.
Volume is a three-dimensional measurement. It measures the total space occupied by the object, which involves multiplying three dimensions (length × breadth × height). This results in cubic units.

Understanding this distinction is crucial for getting the units correct in your final answers.

5. What is a common mistake to avoid when solving RD Sharma problems on the volume of a cuboid with mixed units?

A very common mistake is failing to ensure all dimensions are in the same unit before calculation. For example, if a problem gives the length in meters, breadth in centimetres, and height in meters, you cannot simply multiply the numbers. The correct first step is to convert all dimensions to a single, consistent unit (either all to meters or all to centimetres). Applying the volume formula with mixed units will always lead to an incorrect answer.

6. From a calculation standpoint, what is the key difference when finding the surface area of a cube versus a cuboid?

The key difference is the number of unique measurements you need.

For a cuboid, you need three distinct measurements: length (l), breadth (b), and height (h). You must use the full formula: TSA = 2(lb + bh + hl).
For a cube, all edges are equal. Therefore, you only need one measurement, the side length (a). The cube is a special case of a cuboid where l = b = h = a, which simplifies the formula to TSA = 6a².

7. How do you solve problems that ask for the number of smaller cubes that can be placed inside a larger cuboid box?

This is a volume-based problem that requires a two-step calculation method:

First, calculate the volume of the larger cuboid box using the formula V_box = length × breadth × height.
Second, calculate the volume of one small cube using the formula V_cube = side³.
Finally, divide the volume of the large box by the volume of one small cube: Number of cubes = V_box / V_cube.

Always ensure all dimensions for both the box and the cube are in the same unit before you begin.