Two cubes of edge 1 cm each are kept side by side the volume of resulting cuboid is

Let the edge of each cube be a cm. 

Volume of each cube = a3 cm3

It is given that the volume of each cube is 27 cm3. 

∴ a3 = 27= (3)3

⇒ a = 3 

Thus, length of each edge of the cube = 3 cm 

When two cubes are joined end-to-end, the solid obtained is a cuboid whose length, breadth and height are 6 cm, 3 cm and 3 cm respectively. 

This can be diagrammatically shown as follows: 

Surface area of the cuboid = 2 (lb + bh + hl) 

= 2 (6 cm × 3 cm + 3 cm × 3 cm + 3 cm × 6 cm) 

= 2 × 45 cm2

= 90 cm2

Thus, the surface area of the resulting cuboid is 90 cm2. 

Option 3 : 5488 cm3 and 1960 cm2

Given:

Two cubes of edge 14 cm each are joined end to end to form a cuboid.

Formula Used:

Volume of a cuboid = lbh

Total Surface Area of cuboid = 2(lb + bh + hl)

Where l = length, b = breadth and h = height

Calculation:

The final object becomes a cuboid.

For the cuboid

l = 28 cm

b = 14 cm

h = 14 cm

Volume of a cuboid = lbh

= 28 × 14 × 14 

= 5488 cm3

Total Surface Area of cuboid = 2 (28 × 14 + 14 × 14 + 14 × 28)

= 2 × 14 ( 28 + 14 + 28 )

= 1960 cm2

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Three cubes, each with 4 cm edge, are joined end to end. Then, the total surface area of the resultant cuboid is cm 2

Solution

Dimensions of the cuboid formed :

l = 12 cm b = 4 cm

h = 4 cm

Total surface area of the cuboid formed = 2 $(l\times b+b\times h+l\times h)$

= $2(12\times 4+4\times 4+4\times 12)=224c{m}^2$