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. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  2. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 15, 25 02:46 AM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  3. 5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus

    Jul 15, 25 02:01 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  4. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More

  5. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More