Class 08 Activity – Surface Area of a cube and cuboid

Objective: 

To verify the formula for surface area of a cube and a cuboid. Or to verify the following formulae

Surface area of a cube = 6 (side)2.

Surface area of a cuboid= 2 (length x breadth + breadth x height + height x length)

Materials Required: 

Thick sheets of paper, a pair of scissors, sello tape, geometry box, etc.

procedure: 

(a) Cube:

On a thick sheet of paper, draw a net of a cube., as shown below. It consists of six identical squares. Using a pair of scissors, cut it out.

2. Fold the net along the dotted lines and use sellotape to get a cuboid of 

edge 3 cm.

(b) Cuboid:

On a thick sheet of paper, draw the net of a cuboid as shown below. It consists of 6 rectangles. Using a pair of scissors cut it out.

2. Fold the net and use sellotape to form a cuboid of dimensions 

5 cm x 4 cm x 2 cm.

Observations:

Surface area of the cube obtained in figure 2 is equal to the sum of the areas of all the six squares in fig. 

Side of each square = 3 cm

So, area of 1 square = 32 sq cm.

 Area of 6 squares = 6 x 32 sq cm.

Or surface area of the cube in fig = 6 x 32 sq.cm. 

= 6 x (edge)2  sq. units.

2. Surface area of the cuboid in figure is equal to the sum of the areas of all the six rectangles in fig. Figure consists of :

2 rectangles of dimensions 5 cm x 4 cm.

2 rectangles of dimensions 4 cm x 2 cm and

2 rectangles of dimensions 2 cm x 5 cm.

So, sum of the areas of all the rectangles in figure 

= [2 (5 x 4) + 2 (4 x 2) + (2 x 5)] sq cm.

= 2 [(5 x 4) + (4 x 2) + (2 x 5)] sq cm.

Or surface area of the cuboid in figure 

= 2 [(5 x 4) + (4 x 2) + (2 x 5)] sq cm.

= 2 [length x breadth + breadth x height + height x length] sq units.

Conclusion : 

From the above activity, it is verified that : 

Total surface area of a cube = 6(edge)2

(b) Total surface area of a cuboid 

= 2 [length x breadth + breadth x height + height x length] sq units.