surface area and volume of cube

8/13/2019 Surface Area And Volume Of Cube

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Made by

Priy Ranjan Prakash


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We come across many situations in our daily liveswhere we are required to find the surface areasof solid figures. For example, when we have to

paint the wall of any room, or when we have tomake a cubical box from any given metal sheet,or we have to cover any toy of cylindricalshape. In such cases, we require the surface

area of these to have an estimate of paint orsheet required.


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The lateral Surface area is the surface area of a3D figure, but excluding the area of anybases. ateral rea is often abbreviated L.A.Imagine a soup can. Now cut down the side

of the can and roll it flat. What was thecircumference of the base is now the lengthof a rectangle. To find the area of thisrectangle which is the same as the lateralarea, multiply this length by the width, whichwas the height of the can.


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Surface AreaThe surface area of a figure is the sum of the area of allsurfaces of a figure. Surface Area is often abbreviatedS.A. The surface area of a prism or cylinder is the

lateral area plus the area of each base. Since the basesfor a prism or cylinder are congruent, this is oftenexpressed as twice the area of the base.
http://en.wikipedia.org/wiki/File:Icosahedron.pnghttp://en.wikipedia.org/wiki/File:Dodecahedron.png


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Let us consider a cube as shown above.Let abe the edge of the cube. Then, the Lateral Surface

Area (i.e., the area of 4 standing faces) is given by,

Lateral Surface Area of Cube = 4a2


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Total Surface Area (i.e., area of all six faces) is given by,

Remember that while calculating the lateral surface area,we do not include the areas of the top and bottomsurfaces as shown in the figure.

If we add the areas of top and bottom surface to thelateral surface area, then we will obtain the totalsurface area of the cube.

Surface Area of Cube =6a2


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Can you find the edge of a cube whose total surface area is 216 sq. cm?

Let the edge of the cube = a

It is given that the surface area of the cube is 216 cm2.

We know that the total surface area of a cube is given by 6a2.

6a2 = 216 cm2

= a2 = cm2

= a2 = 36 cm2

= a = 6 cm

Thus, the side of the cube is 6 cm.


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Suppose your mother asks you to go to the market and buy 2.5 litres of milk.

What does this term 2.5 litres represent?

This term represents the amount of milk that you are required to buy from the

market. This is called volume. Hence, 2.5 litres is the volume of the milk.

Therefore, we can say that,

The space occupied by an object is called its volume.The capacity of a container is the volume of the substance that can fill

the container completely.

For example, if a container can be completely filled with 5 litres of milk, it

means that the capacity of the container is 5 litres.

We must have seen cubical, cuboidal and cylindrical shaped objects in our

surroundings like a container, a box, a roller, a room, etc. All these objectshave different capacities or volumes. How can we find the capacity or the

volume of an object?


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To find the volume of solid figures like cube ,we have to know the formulae. Let

us discuss volumes of a cube.Let us consider a cube of edge aas shown below.

The volume of the cube is given by the formula

Volume of Cube = a3


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THE END

surface area and volume of cube

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