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×b+b×h+l×h)
= 2(12×4+4×4+4×12)=224 cm2
2