NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.2

Class VIII Mathematics Ex. 9.2 of Mensuration in PDF file format as well as online format for CBSE session 2024-25. Know here the comparison of volumes of one solid with others. Learn here how to find the areas and volumes of cube and cuboid, how it is related to cylinder or sphere. If someone has doubt to understand the NCERT textbook solutions, please try the videos solution particularly explanation video.

A solid bounded by six rectangular plane faces is called a cuboid. A matchbox, a chalkbox, a tea packet, a brick, a tile, a book, etc., are all examples of a cuboid. A cuboid has 6 rectangular faces, 12 edges and 8 vertices. Any face of a cuboid may be called its base. The four faces which meet the base are called the lateral faces of the cuboid.

A cuboid whose length, breadth and height are all equal is called a cube. Ice cubes, sugar cubes, dice, etc., are all examples of a cube. Each edge of a cube is called its side.

The space occupied by a solid body is called its volume. The standard unit of volume is cubic centimetre, written as cubic cm or cm³.
The volume of a cube of side 1 cm is 1 cm³.
The other units of volume are mm³, dm³, m³, litre, etc.

CUBOID

• (i) Volume of a cuboid = (length x breadth x height) = (l x b x h) cubic units
• (ii) Diagonal of a cuboid = √(l² + b² + h²) units
• (iii) Total surface area of a cuboid = 2 (lb + bh + lh) sq. units
• (iv) Lateral surface area of a cuboid = [2 (l + b) x h)] sq. units

Find the volume, the total surface area and the lateral surface area of a cuboid which is 8 m long, 6m broad and 3.5, high.
Volume of the cuboid = (l x b x h) cubic units
= (8 x 6 x 3.5) m³ = 168 m³
Total surface area of the cuboid = 2 (lb + bh + lh) sq. units
= 2 (8 x 6 + 6 x 3.5 + 8 x 3.5) m²
= 194 m²
Lateral surface area of the cuboid = {2 (l + b) x h} m²
= {2 (8 + 6) x 3.5} m²
= 98 m²

CUBE
(i) Volume of a cube = (edge)³ = a³ cubic units
(ii) Diagonal of a cube = 3a² units
(iii) Total surface area of a cube = (6a²) sq. units
(iv) Lateral surface area of a cube = (4a²) sq. units

Find the total surface area of the cube whose volume is 343 cm. Let the length of each edge of the cube be a cm.
Then, its volume = (a³) cm³
So, a³ = 343 = 7 x 7 x 7
a = 7 cm
So the length of each edge of the cube = 7 cm
Total surface area of the cube = (6a²) sq. units
= (6 x 7 x 7) cm² = 294 cm²

The volume of a reservoir is 180 m. Water is poured into it at the rate of 60 liters per minute. How many hours will it take to fill the reservoir?
Volume of the reservoir = 108 m³
= (108 x 1000) liters (Because 1 m³ = 1000 L)
Time taken to fill the reservoir
t = (volume of the reservoir in liters/ rate of flow in liters per min)
t = (108 x 1000)/60 min. = 1800 min. =1800/60 hrs. = 30 hrs.

How do you find the volume of a cube and cuboid?
Volume of cuboid = length × breadth × height.
Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve.

What is difference between cuboid and rectangular prism?
A cuboid has a square cross-sectional area and a length, that is possibly different from the side of the cross-section. It has 8 vertices, 12 sides, 6 faces. A rectangular prism has a rectangular cross-section. It may not stand vertical, if you make it stand on the cross sectional base.

What’s the difference between a square and a cube?
The basic difference between a cube and a square is, a cube is a 3D figure (having 3 dimensions) i.e. length, breadth and height while a square has only 2 dimensions i.e. length and breadth. The sides (faces) of a cube are squares. The edges are straight lines. The corners (vertices) are at right angles.
What are the similarities between cube and cuboid?
Cube and Cuboid Similarities
(i) A cube and cuboid have six faces.
(ii) They both have 12 edges.
(iii) Cube and cuboid have eight vertices.