Question

two cubes each of 10cm edge are joined end to end. find the surface area of the resulting cuboid.

Answer 1

$\bold{\huge{Answer}}$

$<b><I>==============$

=>When the two cubes of 10cm edge are fixed together, then the new solid formed will be cuboid ...

Whose length = 10 + 10 = 20cm

Breadth = 10 cm

And , Height = 10 cm

Therefore , Total surface area of a cuboid = 2 [lb + bh + lh ]

= 2 [ 20×10 + 10×10 + 20×10 ]
=2[200 + 100 + 200]
=2×500

$then \: the \: answer \: will \: be \:$

$= {1000}^{2} cm$

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Answer 2

$\huge\bf{\boxed{1000 \: cm^2}}$
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There are 2 ways to obtain the answer :

1) Combine the surface area of both the squares.

2) Calculating length, breadth and height of new cuboid formed and then calculating the surface area by its formula.
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$\underline{\large{METHOD: \: 1}}$

In this method, we add the surface areas of both cubes.

Since we have lost 1 side, we lose area = area of square of same edge.

So, => Area of Cube (5 sides only) = $\bf{ 6a^2 - a^2 = 5a^2 }$

where, a = edge of cube

Formula:
$\bf{5a^2 + 5a^2 = 2(5a^2)}$

Substituting value of a = 10 we get,

=> $2(5(10)^2)$

=> $2(5 \times 100)$

=> $2(500)$

=> $\bf{Area \: of \: Cuboid = 1000 cm^2}$

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$\underline{\large{METHOD: \: 2}}$

After the transformation,

Length = 2(edge) = 20cm
breadth = edge = 10cm
height = edge = 10cm

Formula:
$\bf{ T.S.A \: of \: Cuboid = 2(lb + lh + bh) }$

Substituting values of length, breadth and height we get,

$= > 2((20 \times 10) + (20 \times 10) + (10 \times 10)) \\ \\ = > 2(200 + 200 + 100) \\ \\ = > 2(500) \\ \\ = > \bf{Area \: of \: Cuboid = 1000 {cm}^{2}}$
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