Volume of a Cuboid

Cuboid is a solid box whose every surface is a rectangle of same area or different areas.

cuboid will have a lengthbreadth and height.

Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides.

Since volume involves 3 sides it is measured in cubic units.

Units of Volume

Volume of a cuboid = (length × breadth × height) cubic units.

= (l × b × h) cubic units.

   (Since area = ℓ × b)

Volume of a cuboid = area of one surface × height cubic units

Let us look at the given cuboid.

The length of the cuboid = 5 cm

The breadth of the cuboid = 3 cm

The height of cuboid (thickness) = 2 cm

The number of 1 cm cubes in the given cuboid = 30 cubes = 5 × 3 × 2

We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm.

Therefore, volume of a cuboid = length × breadth × height


Solved examples on volume of a cuboid:

1. Find the volume of a cuboid of dimensions 14 cm × 12 cm × 8 cm.

Solution:

Volume of cuboid = length × breadth × height.

Here, length = 14 cm, breadth = 12 cm and height = 8 cm.

Volume of cuboid = 14 × 12 × 8 cubic cm.

= 1344 cubic cm.

Therefore, volume of cuboid = 1344 cubic cm.


2. Michael made a shoe box with length 8 cm, breadth 6 cm and height 6 cm. Find the volume of the box.

Solution:

Volume of the shoe box = Length × breadth × height.

                                   = 8 × 6 × 6

                                   = 288 cu cm.


3. A fish tank is 40 cm long, 15 cm broad and 10 cm high. What is its volume in cu cm?

Solution:

The length of the fish tank = 40 cm

The breadth of the fish tank = 15 cm

The height of the fish tank = 10 cm

Therefore, the volume of the fish tank = length × breadth × height.

                                                        = 40 × 15 × 10 cu. cm

                                                        = 6000 cu cm.


4. Find the volume of a cuboid of dimensions 14 cm × 50 mm × 10 cm.

Solution:

Here, length = 14 cm,

[Given, breadth = 50 mm; we need to convert breadth to same unit and then solve. We know, 10 mm = 1 cm. Therefore, 50 mm = 50/10 cm = 5 cm].

Breadth = 5 cm,

Height = 10 cm.

Volume of cuboid = length × breadth × height.

                          = 14 × 5 × 10

                          = 700 cubic cm.

Therefore, volume of cuboid = 700 cubic cm.

Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve.


5. Find the volume of a cuboid of dimensions 17 mm × 0.2 cm × 12 mm in cu. cm.

Solution:

Given, length = 17 mm.

We know, 10 mm = 1 cm.

= 17/10 cm.

= 1.7 cm.

Therefore, length = 1.7 cm.

Similarly, height = 12 mm.

We know, 10 mm = 1 cm.

= 12/10 cm.

= 1.2 cm.

Therefore, height = 1.2 cm.

Volume of cuboid = length × breadth × height.

Length = 1.7 cm, breadth = 0.2 cm and height = 1.2 cm.

           = 1.7 × 0.2 × 1.2 cu. cm.

           = 0.408 cu. cm.

Therefore, volume of cuboid = 0.408 cubic cm.


6. Find the number of cubical boxes of cubical side 3 cm which can be accommodated in carton of dimensions 15 cm × 9 cm × 12 cm.

Solution:

Volume of box = side × side × side.

                      = 3 × 3 × 3

                      = 27 cu. cm.

Volume of carton = length × breadth × height.

                          = 15 × 9 × 12

                          = 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

                          = 1620/27

                          = 60

Therefore, number of cubical boxes = 60.


7. How many bricks each 25 cm long, 10 cm wide and 7.5 cm thick will be required for a wall 20 m long, 2 m high and 0.75 m thick? If bricks sell at $900 per thousand what will it cost to build the wall?

Solution:

Volume of the wall = 20 m × 2 m × 0.75 m

                           = 20 × 100 cm × 2 × 100 cm × 0.75 × 100 cm

Volume of brick = 25 cm × 10 cm × 7.5 cm

Number of bricks = Volume of the wall/Volume of the brick

                         = 20 × 100 × 2 × 100 × 0.75 × 100/25 × 10 × 7.5

                         = 16000

The number of bricks = 16000

The cost of 1 thousand bricks = $ 900

The cost of building the wall = $ 900 × 16 = $ 14400

Note: While calculating the volume of a cuboid all the dimensions should be changed into the same unit. 


Questions and Answers on Cuboid:

1. Find the volume of each of the cuboids.

(i) Length = 5 cm, Breadth = 4 cm and Height = 3 cm

(ii) Length = 15 m, Breadth = 10 m and Height = 2 m

(iii) Length = 0.5 m, Breadth = 3 m and Height = 4 m

(iv) Length = 3.2 cm, Breadth = 2 cm and Height = 8 cm

(v) Length = 5 m, Breadth = 1.5 m and Height = 1.2 m


Answers:

1. (i) 60 cu cm

(ii) 300 cu m

(iii) 6 cu m

(iv) 51.2 cu cm

(v) 9 cu m


2. Find the volume of these tanks.

(i) Length = 16 cm, Breadth = 60 cm and Height = 20 cm

(ii) Length = 6 m, Breadth = 3 m and Height = 5 m

(iii) Length = 2 m, Breadth = 1.5 m and Height = 1.5 m

(iv) Length = 80 cm, Breadth = 20 cm and Height = 40 cm

(v) Length = 1.2 m, Breadth = 1.2 m and Height = 1 m


Answers:

2. (i) 19200 cu cm

(ii) 90 cu m

(iii) 4.5 cu m

(iv) 64,000 cu cm

(v) 1.44 cu m

Volume.

Units of Volume

Cube.

Cuboid.

Practice Test on Volume.

Worksheet on Volume.





5th Grade Geometry

5th Grade Math Problems

From Volume of a Cuboid to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

    Apr 15, 24 01:29 AM

    LCM of 24 and 30
    We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

    Read More

  2. Common Multiples | How to Find Common Multiples of Two Numbers?

    Apr 15, 24 01:13 AM

    Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

    Read More

  3. Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

    Apr 14, 24 03:06 PM

    Lowest Common Multiple
    The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

    Read More

  4. Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

    Apr 14, 24 02:23 PM

    HCF Using Venn Diagram
    Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…

    Read More

  5. Common Factors | Find the Common Factor | Worksheet | Answer

    Apr 14, 24 02:01 PM

    Common Factors of 24 and 36
    Common factors of two or more numbers are a number which divides each of the given numbers exactly. For examples 1. Find the common factor of 6 and 8. Factor of 6 = 1, 2, 3 and 6. Factor

    Read More