Two identical cubes are placed one over the other what would be the shape of the resultant solid

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150 Questions 100 Marks 180 Mins

Given:

Volume of each identical cube = 64 cm3

And the number of cube = 2

Formula used:

If the cube of a side length x, then the volume of cube = x3

If the cuboid have length(l), breadth(b) and height(h), then total surface area of cuboid = 2 × [(l × b) + (b × h) + (h × l)]

Calculation:

The volume of cube = 64 cm3

⇒ x3 = 64 

⇒ x = 4 cm

But the cuboid is made by joining end to end of the cube then the length of the cuboid will be twice the side length of each cube and the rest breadth and height will remain the same.

Thus, l = 2 × 4 

⇒ l = 8 cm

Breadth(b) = 4 cm

And height = 4 cm

The total surface area of cuboid = 2 × [(8 × 4) + (4 × 4) + (4 × 8)]

⇒ 2 × [32 + 16 + 32]  

⇒ 2 × [80] 

⇒ 160 cm2 

∴ The total surface area of cuboid is 160 cm2

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