# Mathematics - Class 5 / Grade 5

- Volume
### Volume

Math - Class 5 – Volume of figures made of unit cubes / Volume of Cubes and Cuboid / Volume: Word Problems / Introduction to Volume – Key Points/Notes/Worksheets/Explanation/Lesson/Practice Questions Tags: Introduction to Volume of cubes and cuboid for fifth grade, How to calculate the volume? Free downloadable Worksheet PDF on Volume for class 5, Lesson on Volume for 5th standard, Volume word problems practice page for grade V, Measurement Unit: Volume for grade 5, Find the volume of a cube and cuboid for class 5, Practice questions with solution on Volume, Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units, Metric Volume, Examples showing how to calculate volume, Definition of volume, cube and cuboid, Formula of volume, Volume by counting cubes, Illustrations, Find the volume of a cube whose edge is 10 cm long. Find the volume of a cube of side 15 cm. Calculate the volume of water that can be stored in a cubical tank whose each side measure 50 cm from inside. Find the volume of a cube of side 10 cm in cubic meters. Find the volume of a cuboid of dimensions 200 mm × 8 cm × 150 mm. Find the volume of a cuboid of dimensions 8000 mm × 900 cm × 12 m. Find the volume of oil that can be stored in a container of dimensions 15 cm × 10 cm × 11 cm. A cuboid measures 27 cm x 18 cm x 9cm. How many cuboids of dimensions 9 cm x 3 cm x 1 cm can be cut from it?Volume

The space occupied by any object is called the

__volume__. Volume is three dimensional. To measure the volumes we need to know the measure of 3 sides. Since, volume involve involves__3 sides, so it is measured in cubic units.__Surface like the page of a book, blackboard, etc. are

__called plane surfaces__. They do not have any volume but have only area.**A cube**is a solid box whose each surface is a square of same area.Therefore, cube has: 6 surfaces or faces, 8 vertices, 12 edges or sides of equal length. Volume of a cube with side length 1 unit is 1 cubic unit. Such cube is called a "

__unit cube__," and used as unit of volume.Volume of a cube

A cube has all sides are of equal length,

So,

__Volume of a cube__= side x side x side = S x S X S cu units

Or

= length x length x length = l x l x l cu units

Or

= area x side cu units (And we know that area of square = side x side)

**Volume of a cuboid**Similarly,

**a cuboid**is a solid box whose every surface is a rectangle of same area or different areas. A cuboid has length, breadth and height.So, Volume of a cuboid

= length x breadth x height = l x b x h cubic units

Or

= area of one surface x height cu units (as area =l x b)

**Note:**In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and solve.**Volume by counting cubes****Step:**Find out the number of unit cubes that form the solid or fill up the entire space occupied by the given solid such as cuboid and cube.Example:

Take an empty cube shaped box of edge 4 cm with open top. Now fit cubes of edges 1 cm in it.

__How many cubes of 1 cm can be fitted into cube box of edge 4 cm?__From the observation, it is clear that 64 such cubes will fit into it. So the volume of the box will be equal to the volume of 64 unit cubes together.

Therefore, the volume of the cube = 64 cu cm

Note that 64 = 4 × 4 × 4

Illustration 1: Find the volume of a cube of side 8 cm.

__Solution:__Volume of cube = l x l x l = 8 x 8 x 8 = 512 cu cmIllustration 2: Find the volume of a cuboid of dimensions 16 cm x 10 m x 6 cm.

__Solution:__Volume of cuboid = l x b x h = 16 x 10 x 6 = 960 cu cmIllustration 3: Find the volume of a cuboid of dimensions 18 cm x 30 mm x 15 cm.

__Solution:__l = 18 cm,

b = 30 mm = 3 cm (10 mm =1 cm, 30/10 = 3 cm),

h = 15 cm

Volume of cuboid = l x b x h

= 18 x 3 x 15

= 810 cu cm

Illustration 4: Find the volume of a cuboid of dimensions 21 mm x 2 cm x 12 mm in cu. cm.

__Solution:__10 mm = 1 cm

Therefore, 21 mm = 21/10 cm = 2.1 cm

And 12 mm = 12/10 = 1.2 cm

Length = 2.1 cm, breadth = 2 cm, height = 1.2 cm

Volume of cuboid = l x b x h

= 2.1 x 2 x 1.2

= 5.04 cu cm

Illustration 5: Find the number of cubical boxes of cubical side 5 cm, which can be accommodated in carton of dimensions 25 cm x 10 cm x 15 cm.

__Solution:__Volume of cubical box = side x side x side

= 5 x 5 x 5

= 125 cu cm

Volume of carton = 25 x 10 x 15

= 3750 cu cm

No. of boxes = Volume of carton/Volume of each box

= 3750/125

= 30