Methods for Determining Volume and Surface Area of Cube Container and Comparison with Cuboid and Triangular Prism Containers

This article discusses the different methods for determining the volume and surface area of a cube container, including using lengths, surface area, and diagonals. It also compares the cube container to cuboid and triangular prism containers, with calculations for their volume and surface area. The article includes step-by-step procedures and examples for each method.

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 lengths1
1. 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
2. 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 = L3)
In our case
10 cm * 10 cm * 10 cm = 1000 cm3
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 = 1000
1000
= 1 litre
1 Hassan Dutsinma, sada. Effective methods of teaching volume of 3-Dimensional shapes methods of teaching
volumes of cube, cuboid and cylinder. pp 5-10
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Method 2
Determination of volume of cube from surface area
1) Determination of cube surface area
The total surface area of the cube is equal to 6*(length by length)
In our case
600 cm2
2)
Since the total cube area of the six faces is 600 cm2 we divide the total surface area by
six to determine area of one face which is equal to
600
6 =100 cm2
3) 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
√ 100 c m2 = 10 cm
4) 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 cm3
5) 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 = 1000
1000
2

= 1 litre
Method 3
Determination of volume of the cube from the diagonals
a. Dividing the diagonals across one of the cubes face by √ 2 to find the cube side length
We know that the diagonal of a perfect square is equivalent to √2 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 √2
In our case diagonal is 10 cm
Length of side = 10
√ 2
= √ 4∗5
√ 2
Dividing the √4 by √2 = 2
Length of one side = 2 * 5 = 10 cm
b. 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 cm3
c. 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 = 1000
1000
3

= 1 litre
Determination of the surface area
Procedure
I. Measure the length of one side of the cube this is because the dimensions are equal
In our case is 10 cm
II. Find the area of one side of the cube
In our case is 10 cm * 10 cm = 100cm2
III. Multiply the area of one face of the cube by six, since there are six faces
Total area = 6 *100 cm2
= 600 cm2
Sketch Net of the cube
Other two commercial containers
1. cuboid container
2. triangular prism container
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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 cm2
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 = 1000
1000
= 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 cm2 * 2 = 400 cm2
10 cm * 5 cm = 50 cm2 * 2 = 100 cm2
20 cm * 5 cm = 100 cm 2 * 2 = 200 cm2
 add the area determine together to determine the total surface area of the cuboid
Total surface area = 400 cm2 + 100 cm2 + 200 cm2 = 700 cm2
Triangular Prism container
Dimensions
5

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 * length2
= 1
2∗50 cm∗10 cm∗4 cm
= 1000 cm3
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 = 1000
1000
= 1 litre
Surface area of the triangular prism3
Procedure
 Determine the area of the of two triangular area
Triangular areas = 1
2∗50 cm∗10 cm* 2 = 500 cm2
 Determine the area of the three rectangles
Area of the first rectangular = 10 cm * 4 cm = 40 cm2
Area of the second and third rectangle
Hypothesis dimension = √ bas e2 +heigh t2
= √ 502 +102
= 500.1 cm
Total area = 500.1 * 4 *2 = 4000.8 cm2
 Total surface area
2 Delta Education(film).A clear view of area and volume formulas: Activities, visuals, masters, 1994
3 Leech, B. C. Prism, 2007
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500 cm2 + 4000.8 cm2
= 4500.8 cm2
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.
Section 2
Included on the excel files uploaded
Bibliography
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)
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