Question

The surface area of a cuboid is 112
c
m
2
. Its length is twice its breadth and its height is half its breadth. If it is melted to form 2 identical cubes without any wastage, what is the volume (in
c
m
3
) of each cube?​

Answer 1

Given : The surface area of a cuboid is 112 cm² .

length is twice its breadth and its height is half its breadth.

melted to form 2 identical cubes without any wastage,

To Find : what is the volume of each cube

Solution:

Let say height =  h   cm

breadth = 2h  cm

Length = 2(2h) = 4h   cm

Surface Area = 2 ( 4h.2h + 2h.h + 4h.h)

= 2(8h² + 2h² + 4h²)

= 28h² cm²

28h² = 112

=> h² = 4

=> h = 2

Volume  = 4h.2h.h  = 8h³

=8*2³

= 64 cm³

melted to form 2 identical cubes without any wastage

Volume of each cube = 64/2 = 32  cm³

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Answer 2

• First Let's Find Surface Area of Cuboid

Surface Area of Cuboid = 2 (lb + bh + lh)

⇒ Surface Area of Cuboid = 2 [(l × b) + (b × h) + (l × h)]

⇒ Surface Area of Cuboid = 2 [(2b × b) + (b × 1/2 b) + (2b × 1/2 b)]

⇒ Surface Area of Cuboid = 2 [(2b²) + (b²/2) + (2b²/2)]

⇒ Surface Area of Cuboid = 2 [2b² + (b²/2) + b²]

⇒ Surface Area of Cuboid = 2 [3b² + (b²/2)]

⇒ Surface Area of Cuboid = 6b² + b²

⇒ Surface Area of Cuboid = 7b² cm²

Substituting the value of Surface Area of Cuboid

⇒ 112 cm² = 7b² cm²

⇒ 112 = 7b²

⇒ 112/7 = b²

⇒ 16 = b²

⇒ √16 = √b²

⇒ 4 = b

⇒ b = 4

________________________________________

Volume of 2 Cubes = Length × Breadth × Height

⇒ Volume of 2 Cubes = 2b × b × 1/2 b

⇒ Volume of 2 Cubes = 2b² × 1/2 b

⇒ Volume of 2 Cubes = b² × 1b

⇒ Volume of 2 Cubes = b³

Substitute the Value of b

⇒ Volume of 2 Cubes = 4³

⇒ Volume of 2 Cubes = 64 cm³

⇒ Volume of  Cube = 64 cm³/2

⇒ Volume of  Cube = 32 cm³