Question

4 cubes of lateral surface area 256 sq cm. are stacked back to back. Find the dimensions and total
surface area of the cuboid thus formed.
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Answer 1

Answer:

Total surface area = 1152cm²

Step-by-step explanation:

given, LSA of the cube = 256 cm²  = 4a² (where a is the side of the cube)

=> 4a² = 256

=> a² = 256/4 = 64

=> a = √64 = 8cm

if 4 cubes are stacked back to back then, a cuboid is formed of length = 4a

= 4*8cm

= 32cm

we know that the breadth = height = 8cm (sides of the cube)

so, the dimension of the cuboid is 32cm x  8cm  x  8cm

TSA of the cuboid = 2(lb+bh+lh) sq.units

                               = 2(32*8 + 8*8 + 32.8) cm²

                               = 2(256 + 64 + 256) cm²

                               = 2(576) cm²

                               = 1152cm²