Question

Arrange 64 unit cubes in as many ways as you can to form a cuboid. Find the surface area of each arrangement. Can solid cuboid of same volume have same surface area?

Answer 1

No. of cuboids are formed using 64 unit cubes

 64 = 1 × 64 ……. (1) 

= 2 × 32 …….. (2) 

= 4 × 16 …….. (3) 

1) l = 64 cm, b = 1 cm, h = 1 cm. 

The total surface area of a cuboid, A = 2(lb + bh + lh) 

= 2 (64 × 1 + 1 × 1 + 1 × 64) 

= 2(64 + 1 + 64)

= 2 × 129 

= 258 Sq. cm.

2) l = 32 cm, b = 2 cm, h = 1 cm.

 A = 2(lb + bh + lh) 

= 2(32 × 2 + 2 × 1 + 32 × 1) 

= 2(64 + 2 + 32) 

= 2 × 98 

= 196 Sq. cm. 

3) l = 16 cm, b = 4 cm, h = 1 cm. 

A = 2(lb + bh + lh) 

= 2(16 × 4 + 4 × 1 + 16 × 1) 

= 2(64 + 4 + 16) 

= 2 × 84 

= 168 Sq. cm.

No, the volume of a cuboid is not same as the surface area of a cuboid.