Class 09 To form a cuboid and find the formula for its surface area experimentally.

 

Activity 27 

OBJECTIVE	MATERIAL REQUIRED
To form a cuboid and find the formula	Cardboard, cellotape, cutter, ruler,
for its surface area experimentally.	sketch pen/pencil.

 METHOD OF CONSTRUCTION

 1.    Make two identical rectangles of dimensions a units × b units, two identical rectangles of dimensions b units × c units and two identical rectangles of dimensions c units × a units, using a cardboard and cut them out.

 2.   Arrange these six rectangles as shown in Fig. 1 to obtain a net for the cuboid to be made.

 3.   Fold the rectangles along the dotted markings using cello-tape to form a cuboid [see Fig. 2].

DEMONSTRATION

 Area of a rectangle of dimensions ( a units × b units) = ab square units.

 Area of a rectangle of dimensions ( b units × c units) = bc square units.

 Area of a rectangle of dimensions ( c units × a units) = ca square units.

 Surface area of the cuboid so formed

 = (2 × ab + 2 × bc + 2 × ca) square units = 2 (ab + bc + ca) square units.

 OBSERVATION

 On actual measurement:

 a  = .....................,              b = .....................,         c = .....................,

 So, ab = .....................,            bc = .....................,      ca = .....................,

 2ab = .....................,         2bc = .....................,    2ca = .....................

 Sum of areas of all the six rectangles = ..............

 Therefore, surface area of the cuboid = 2 (ab+bc+ca)

APPLICATION

This result is useful in estimating materials required for making cuboidal boxes/almirahs, etc