Back to: Mathematics Primary 5

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Volume is measured in “cubic” units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box.

Volume of Cubes:

This is a unit cube. It occupies space. The space it occupies is called its volume. The volume of the cube is 1 cubic centimeter, because the length of its sides is 1 cm. (1 unit cube) and its volume is 1 cubic centimeter or 1 cm³.

This figure is made up of three units joined together. The volume is 3 cubic cm (3cm³). Each unit cube is 1 cub.cm and there are three such unit cubes. Thus, we find the volume by counting the number of unit cubes.

 

Definition of a Cube: A cube is a special type of cuboid whose length, breadth and height are equal. Each face of the cube is a square and all angles are right angles. Cube is thus a special case of a cuboid. It is also called a square prism.

Properties of a Cube:

1. It has six faces
2. All the faces are congruent
3. Each face is parallel to the one opposite to it
4. Has 12 edges and 8 vertices

 

Volume of Cube:

The volume of a cube defines the number of cubic units, occupied by the cube completely. A cube is a solid three-dimensional figure, which has 6 square faces or sides. To calculate the volume we should know the dimensions of the cubeThe equation to find the volume of a cube is length by width by height. The volume of any shape is the amount of space the object uses.

Example:  A box 4 in. wide, 3 in. high, and 12 in. long, uses 144 in.³ of space.

Finding the volume of a perfect cube, the equation of calculating the volume is:

The volume of a perfect cube is equal to y³ or  y ^. y ^. y .

Solve the volume of a rectangular cube that has the following qualities:

Width:15 cm.
Length:7 cm.
Height:4 cm.

 

                          The formula for a cube is l³

 

Question 1: Find the volume of the cube, having the sides of length 7 cm.

Solution:

Given, the length of sides of the cube is 7 cm.

We know, Volume of a cube = (length of sides of the cube)³

Therefore, Volume, V = (7 cm)³

V = 343 cm³

Question 2: Find the length of the edges of the cube, if its volume is equal to 125 cm³.

Solution:

Given, Volume of the cube = 125 cm³.

Let the length of the edges is ‘a’.

We know, by the formula,

The volume of a cube = (length of edges of the cube)³

Substituting the value, we get,

125 = a³

Or a = ³√125

Or a = 5 cm

Therefore, the length of the cube is 5 cm.

 

 

Volume of Cuboids

Definition of a Cuboid: A cuboid is a rectangular prism with six rectangular faces and all angles are right angles. It can also be called a square prism if at least two of the lengths are equal.

Properties of a cuboid:

1. It has 6 faces
2. Each face is congruent and parallel to the one opposite to it.
3. It has 12 edges and 8 vertices

Volume of a Cuboid

Volume of a Cuboid is a measurement of the occupied units of a cuboid. The volume of a cuboid is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a cuboid is the number of units used to fill a cuboid.

Volume is the space inside a 3 dimensional shape

A cuboid is a 3 dimensional shape. Therefore to work out the volume, we need to know the 3 measurements. The volume is found using the formula

 

Volume = Height x Width x Depth ( V = h x w x d)

 

Examples:

1. Find the volume of the cuboid in the figure below:

Solution:

Length of the cuboid   = 5 cm

Breadth of the cuboid = 4 cm

Height of the cuboid   = 2 cm

Volume = (5 x 4 x 2)cm³

= 40 cm³

2. A box is 9 cm long, 5 cm wide and 2 cm high. Find its volume.

Solution:

Length of a box       = 9 cm

Breadth of the box = 5 cm

Height of the box   = 2 cm

Volume of the box = Length x Breadth x Height

= (9 x 5 x 2)cm³

= 90 cm³

3. The length of a rectangular block is 15 cm, its breadth is 10 cm and height is 8 cm. Find the volume of the block.

Solution:

Length of a rectangular block       = 15 cm

Breadth of the rectangular block = 10 cm

Height of rectangular block          = 8 cm

Volume of rectangular block        = Length x Breadth x Height

= (15 x 10 x 8) cm³

= 1,200 cm³

 

Volume of a Cylinder

A cylinder is a solid composed of two congruent circles in parallel planes, their interiors, and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions.

The volume of a 3-dimensional solid is the amount of space it occupies.  Volume is measured in cubic units ( in3, ft3, cm3, m3, et cetera).  Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a cylinder with radius r is the area of the base B times the height h

V=Bh  or  V=πr2h

 

Volume of a Cylinder

Example : Find the volume of the shape below:

Solution

The shape is a cylinder.

Volume of a cylinder = area of a circle  height of prism

Area of circle =

= 3.14 4  4

= 50.24cm²

Volume of cylinder = 50.54  15

Volume of prism = 753.6cm³

 

 

Example:

Find the volume of the cylinder shown. Round to the neatest cubic centimeter.

Solution

The formula for the volume of a cylinder is V=Bh  or  V=πr2h

The radius of the cylinder is 8cm and the height is 15cm.

Substitute 8

for r and 15 for h in the formula V=πr2h

V=π(8)2(15)

Simplify.

V=π(64)(15)≈3016

Therefore, the volume of the cylinder is about 3016 cubic centimeters.

 

Quiz

1. A cylinder has height 5 centimeters and radius 3 Find the 1. volume
2. Mention three 3d shapes as well as their properties

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