Arrange 64 unit cubes in as many ways as you can to form a cuboid. Fin

1.	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» 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.

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»

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.