Subscribe to our YouTube channel for the latest videos, updates, and tips.


Volume of Cubes and Cuboids

In volume of cubes and cuboids we will discuss how to calculate volume in different questions.


What is a Volume?

The volume of any 3-dimensional solid figure is the measure of space occupied by the solid. In case of a hollow 3-dimensional figure, the volume of the body is the difference in space occupied by the body and amount of space inside the body. 

We also come across different hollow objects in our daily life. These hollow objects can be filled with air or liquid that takes the shape of the container. Here, the volume of the air or the liquid that the interior of the hollow object can accommodate is called the capacity of the hollow object. 

Thus, the measure of space an object occupies is called its volume. The capacity of an object is the volume of substance its interior can accommodate. 

 The units for measuring volume are cubic units, i.e., cm², m², etc. 

 The volume can be measured in litres or milliliters. In such cases, volume is known as capacity. 


Standard Unit of Volume:

Volume is always measured in cubic units. The standard unit volume is 1 cm³ but there are various other units of measurement of length like m, dm, dam, etc., so we have many other standards of measurement of volume.

Let’s observe the chart to understand the relation between the various units of volume.

standard unit volume,volume of cuboid



Cuboid:



volume of cuboid,standard unit volume

A cuboid is made of six rectangular regions called faces. It has 6 faces. They are ABCD (top face), EFGH (bottom face), ABGH (front face), DEFC (back face), ADEH and BCFG are side faces. 


Thus, a cuboid is made up of 3 pairs of congruent rectangular faces (top, bottom); (front, back); (side face). 


Face EFGH is called the base of the cuboid. 
Front face ABGH, back face DEFC and side faces ADEH and BCFG are called the lateral faces of the cuboid. 


Any two faces other than opposite faces meet in a line segment which is called an edge of the cuboid. The cuboid has 12 edges AB, BC, CD, DA, EF, FG, GH, HE, AH, BG, DE and CF. The three edges meet at a common point called the vertex. A cuboid has 8 vertices, namely A, B, C, D, E, F, G and H. 


Now we will discuss about the volume of cubes and cuboids.



Volume of cuboid: 


Let l, b, h represent length, breadth and height of the cuboid.

Area of the rectangular base EFGH of the cuboid = l × b.

Volume of the cuboid = (Area of base) × (height of the cuboid) = (l × b) × h = lbh

Let us consider a cuboid of length ‘l’, breadth ‘b’ and height ‘h’.

Then the volume of the cuboid is given by …………

Volume = length × breadth × height

Length of cuboid = Volume/(breadth × height)

Breadth of the cuboid = Volume/(length × height)

Height of the cuboid = Volume/(length × breadth)


Note:

While finding the volume of cuboid, length, breadth and height must be expressed in the same units.


Volume of cube:

It is a special type of cuboid whose length, breadth and height are equal. So, the volume of the cube whose edge is l is expressed as ……….

Volume of the cube = l × l × l = l³

Note:

If the length of the cube or the edge is 1 unit, then it is referred to as 1 unit cube.



 Volume and Surface Area of Solids

Volume of Cubes and Cuboids

Worked-out Problems on Volume of a Cuboid




7th Grade Math Problems 

8th Grade Math Practice 

From Volume of Cubes and Cuboids 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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Speed Distance and Time | Relation between Speed Distance and Time

    May 21, 25 12:58 PM

    Speed is defined as the distance covered per unit time. Speed = (Distance Travelled)/(Time Taken) Or, S = D/T. Speed also requires a unit of measurement. If the distance is in kilometres

    Read More

  2. Math Problem Answers | Solved Math Questions and Answers | Free Math

    May 21, 25 12:45 PM

    Partial fraction
    Math problem answers are solved here step-by-step to keep the explanation clear to the students. In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades

    Read More

  3. Test of Divisibility | Divisibility Rules| Divisible by 2, 3, 5, 9, 10

    May 21, 25 10:29 AM

    The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not. Test of divisibility by 2: A number is divisible by 2

    Read More

  4. Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

    May 21, 25 10:17 AM

    Divisible by 7
    Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

    Read More

  5. Average Word Problems | Worksheet on Average Questions with Answers

    May 20, 25 05:40 PM

    In average word problems we will solve different types of problems on basic concept of average. 1. Richard scored 80, 53, 19, 77, 29 and 96 runs in 6 innings in a series. Find the average runs scored…

    Read More