Question

arrange. 64cubes of equal size as many ways as you can to form a cuboid.find the surface area of each arrangement.can solid shapes of same volume have same surface area?​

Answer 1

No , solid shapes of same volume does not have necessarily same surface area

Step-by-step explanation:

64cubes of equal size ( assuming 1 cm *  1 cm  * 1  cm  each)

= 4 * 4 * 4    is Cube  ( Special form of cuboid)

                             Volume cm³                Surface area cm²

4 * 4 * 4                       64                             96

1 * 1 * 64                       64                             258    

1 * 2  * 32                     64                             196

1 * 4 * 16                       64                             168

1 * 8 * 8                        64                             160

2 * 2 * 16                      64                             136

2 * 4 * 8                        64                             112

Here volume is same in each case but surface area is different

No , solid shapes of same volume does not have necessarily same surface area

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

64cubes of equal size ( assuming 1 cm * 1 cm * 1 cm each)

= 4 * 4 * 4 is Cube ( Special form of cuboid)

Volume cm³ Surface area cm²

4 * 4 * 4 64 96

1 * 1 * 64 64 258

1 * 2 * 32 64 196

1 * 4 * 16 64 168

1 * 8 * 8 64 160

2 * 2 * 16 64 136

2 * 4 * 8 64 112

Here volume is same in each case but surface area is different

No , solid shapes of same volume does not have necessarily same surface area