### Introduction

Volume is a measure of space

The shape of cube container is chosen since it has only one similar parameter which is similar for all the sides, and does not vary, hence the effect on one will have similar effect on the other remaining two sides.

### Description of a cube container

A cube is a regular shaped object that three dimension with equal measurements of width, length and height.

A cube has six equal square faces of which their lengths are equal and meet at right angle

Procedure of determining a volume of a cube

Method 1

Determination of volume from lengths

- Determination of length of one side of the cube container

Using a ruler or measuring tape to measure the side of the cube

In our case the length measured using a piece of ruler is 10 cm

- Determination of volume

After determining the length of one side of the cube, cube the value that is multiply the number by itself thrice, meaning we multiply length by length by length ( L * L * L = L^{3})

In our case

10 cm * 10 cm * 10 cm = 1000 cm^{3}

- Conversion of the cubic centimeter to litres

1 litre = 1000 milliliters

But

1 cubic centimeter = 1 milliliters

Hence

1 litre = 1000 cubic centimeter

Therefore

The capacity =

= 1 litre

### Determination of volume of cube from surface area

- Determination of cube surface area

The total surface area of the cube is equal to 6*(length by length)

In our case

600 cm^{2}

Since the total cube area of the six faces is 600 cm^{2} we divide the total surface area by six to determine area of one face which is equal to

cm^{2}

- Finding the square-root of the one face surface area

In order to determine the lengths of the sides of one face of the cube which are equal we will find the square-root

= 10 cm

Cube the value determined of the length of the cube in order to determine the volume of the cube

10 cm by 10 cm by 10 cm = 1000 cm^{3}

- Conversion of the units into litres

1 litre = 1000 milliliters

But

1 cubic centimeter = 1 milliliters

Hence

1 litre = 1000 cubic centimeter

Therefore

The capacity =

= 1 litre

### Determination of volume of the cube from the diagonals

- Dividing the diagonals across one of the cubes face by to find the cube side length

We know that the diagonal of a perfect square is equivalent to by the length of one side

Therefore if possibly you have only the diagonal dimension of one face of the cube, then the length of the cube will be determined by dividing the diagonal length with

In our case diagonal is 10 cm

Length of side =

=

Dividing the = 2

Length of one side = 2 * 5 = 10 cm

- Volume of the cube

Cube the value determined of the length of the cube in order to determine the volume of the cube

10 cm by 10 cm by 10 cm = 1000 cm^{3}

- Conversion of the units into litres

1 litre = 1000 milliliters

But

1 cubic centimeter = 1 milliliters

Hence

1 litre = 1000 cubic centimeter

Therefore

The capacity =

= 1 litre

### Determination of the surface area

Procedure

- Measure the length of one side of the cube this is because the dimensions are equal

In our case is 10 cm

- Find the area of one side of the cube

In our case is 10 cm * 10 cm = 100cm^{2}

- Multiply the area of one face of the cube by six, since there are six faces

Total area = 6 *100 cm^{2}

= 600 cm^{2}

### Other two commercial containers

- cuboid container
- triangular prism container

Cuboid container

Dimensions of the cuboid to give a capacity of 1 litre

Length = 10 cm

Width = 20 cm

Height = 5 cm

Volume of cuboid = length by width by height

Volume of the cuboid = 10 * 20 * 5

= 1000 cm^{2}

Conversion of the units into litres

1 litre = 1000 milliliters

But

1 cubic centimeter = 1 milliliters

Hence

1 litre = 1000 cubic centimeter

Therefore

The capacity =

= 1 litre

### Surface area of the cuboid

Procedure

- determine the area of one face and multiply by two to represent total area of two opposite faces that are equal in each of the three dissimilar faces

In our case

10 cm *20 cm = 200 cm^{2} * 2 = 400 cm^{2}

10 cm * 5 cm = 50 cm^{2} * 2 = 100 cm^{2}

20 cm * 5 cm = 100 cm ^{2} * 2 = 200 cm^{2}

- add the area determine together to determine the total surface area of the cuboid

Total surface area = 400 cm^{2} + 100 cm^{2} + 200 cm^{2} = 700 cm^{2}

Triangular Prism container

### Dimensions

Cross-section area dimensions

- Base = 10 cm
- Height = 50 cm

Length of the prism = 4 cm

Volume of the prism container is determined by multiplying the cross section area by length

Volume = cross-section area * length

= 1000 cm^{3}

Conversion of the units into litres

1 litre = 1000 milliliters

But

1 cubic centimeter = 1 milliliters

Hence

1 litre = 1000 cubic centimeter

Therefore

The capacity =

= 1 litre

Surface area of the triangular prism

Procedure

- Determine the area of the of two triangular area

Triangular areas = * 2 = 500 cm^{2}

- Determine the area of the three rectangles

Area of the first rectangular = 10 cm * 4 cm = 40 cm^{2}

Area of the second and third rectangle

Hypothesis dimension =

= 500.1 cm

Total area = 500.1 * 4 *2 = 4000.8 cm^{2}

500 cm^{2} + 4000.8 cm^{2}

= 4500.8 cm^{2}

### Comparison of the tree containers

From the calculation of areas for the three containers we found out that the area of the triangular prism has the highest surface area as compared to cuboid and cube though their volume are equal that is a volume of 1litre.

Reduction of the surface area with an equal percentage will effectively minimize the cost of material used when building the cube as compared to the other two containers

The design of a cube and cuboid is more appropriate in opening and pouring as since they both have flat surfaces, compared to the triangular prism.

Included on the excel files uploaded

## References

Dutsinma, Hassan, s, Effective methods of teaching volume of 3-Dimension shapes methods of teaching volumes of cube, cuboid and cylinder, (LAP LAMBERT Academic publishing, 2014)

Delta Education (film), A clear view of area and volume formulas: Activities, visuals, masters. Nashua, (NH: Delta Education, 1994)

B, C, Leech, Prism, (New York: Rosen Pub. Groups Powerkids press, 2007)