Question

The surface area of
a cuboid is 112 cm
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 cm") of each
cube?​

Answer 1

Answer:  32 cm

Step-by-step explanation:

For cuboid:

T.S.A = 112cm^2

Let b = x cm

then, l = 2x cm

h = x/2 cm

A/q

T.S.A = 112cm^2

2 (lb + lh + bh) = 112

=> lb + lh + bh = 112 / 2

=> lb + lh + bh = 56

=> 2x * x + 2x * x / 2 + x * x / 2 = 56

=> 2x^2 + x^2 + x^2 / 2 = 56

=> ( 4x^2 + 2x^2 + x^2 ) / 2 = 56

=> 4x^2 + 2x^2 + x^2  = 56 * 2

=> 7x^2 = 56 * 2

=> x^2 = ( 56 * 2 ) / 7

=> x ^ 2 = 16

=> x ^2 = 4 ^ 2

=> x = 4

//

For cuboid,

=> b = x = 4cm

    l = 2x = 2 * 4cm = 8cm

    h = x/ 2 = 4 / 2cm = 2cm

Now,

Volume = l * b * h

   = 4 * 8 * 2

   = 64 cm ^ 3

As per the question, 2 identical cubes are formed .

So,  their volumes are same

Volume of cube = a ^ 3

Since there are 2 cubes, therefore

64 = 2 ( a^3)

=> 64 / 2 = a^3

=> a^3 = 32 cm ^ 3

Where a^3 = volume of the each cubes

Hence, volume of each cube will 32 cm .

Answer 2

Given:

The surface area ofa cuboid is 112 cm its length is twice its breadth and its height is half its breadth. It is melted to form 2 identical cubeswithout any wastage.

To find:

Volume of each cube ?

Calculation:

Let us consider that breadth (width) be x , therefore height will be ½(x) and length will be 2x.

Now, the net surface area is 112 cm² .

$\therefore \: 2 \bigg(lb + bh + lh \bigg) = 112$

$\implies \: (x)( \dfrac{x}{2}) + (x)(2x) + (2x)( \dfrac{x}{2} )= 56$

$\implies \:\dfrac{ {x}^{2} }{2} + 2 {x}^{2} + {x}^{2} = 56$

$\implies \:\dfrac{ {x}^{2} }{2} + 3 {x}^{2}= 56$

$\implies \:\dfrac{ 7{x}^{2} }{2} = 56$

$\implies \:{x}^{2} = 16$

$\implies \:x = 4 \: cm$

Now , breadth is 4 cm , so height will be 4/2 = 2cm, and length will be (4×2) = 8 cm.

Now, volume of the cuboid be V :

$\therefore \: V = l \times b \times h$

$\implies \: V = 8 \times 4 \times 2$

$\implies \: V = 64 \: {cm}^{3}$

Now, the whole cuboid is melted to produce two cubes without any wastage :

So, volume of cube will be :

$\therefore \: V_{cube} = \dfrac{V}{2} = \dfrac{64}{2} = 32 \: {cm}^{3}$

So, volume of each cube is 32 cm³.