Question

2 cubes each of volume 64 cm are joined end to end. Find the surface area of the resulting cuboid. ​

Answer 1

${\huge{\sf{\underline{\red{Given :}}}}}$

2 cubes each of volume 64 cm are joined end to end.

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${\huge{\sf{\underline{\blue{To Find:}}}}}$

Find the surface area of the resulting cuboid.

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${\huge{\sf{\underline{\orange{Formula \: used :}}}}}$

${\sf{volume \: of \: cuboid \: = {side}^{3} } }$

${\sf{area \: of \: cuboid =2(lb + bh + hl) }}$

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${\huge{\sf{\underline{\green{Solution :}}}}}$

Let the sides of cube be x.

${\sf{Volume \: of \: 1 \: cube = {64}^{3} }}$

${\sf{ {side}^{3} = {64cm}^{3} }}$

${\sf{ {a}^{3} = {4}^{3} }}$

${\sf{a = 4}}$

Than,

Length of cuboid = a + a = 4cm + 4cm = 8cm

Breadth = a = 4cm

Height = a = 4cm

Hence,

Length = 8cm, Breath = 4cm, Height = 4cm

${\sf{area \: of \: cuboid =2(lb + bh + hl) }}$

${\sf{ = 2(8 \times 4 + 4 \times 4 + 4 \times 8}}$

=2(32 +16 +32)

=2(80)

${\mathfrak{\red{\boxed{=160 {cm}^{3} }}}}$

So,

${\mathfrak{\red{The \: area \: of \: cuboid \: is \: 160 {cm}^{3} .}}}$

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Answer 2

Answer:

2 cubes each of volume 64 cm are joined end to end.

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{\huge{\sf{\underline{\blue{To Find:}}}}}

ToFind:

Find the surface area of the resulting cuboid.

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{\huge{\sf{\underline{\orange{Formula \: used :}}}}}

Formulaused:

{\sf{volume \: of \: cuboid \: = {side}^{3} } }volumeofcuboid=side

3

{\sf{area \: of \: cuboid =2(lb + bh + hl) }}areaofcuboid=2(lb+bh+hl)

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{\huge{\sf{\underline{\green{Solution :}}}}}

Solution:

Let the sides of cube be x.

{\sf{Volume \: of \: 1 \: cube = {64}^{3} }}Volumeof1cube=64

3

{\sf{ {side}^{3} = {64cm}^{3} }}side

3

=64cm

3

{\sf{ {a}^{3} = {4}^{3} }}a

3

=4

3

{\sf{a = 4}}a=4

Than,

Length of cuboid = a + a = 4cm + 4cm = 8cm

Breadth = a = 4cm

Height = a = 4cm

Hence,

Length = 8cm, Breath = 4cm, Height = 4cm

{\sf{area \: of \: cuboid =2(lb + bh + hl) }}areaofcuboid=2(lb+bh+hl)

{\sf{ = 2(8 \times 4 + 4 \times 4 + 4 \times 8}}=2(8×4+4×4+4×8

=2(32 +16 +32)

=2(80)

{\mathfrak{\red{\boxed{=160 {cm}^{3} }}}}

=160cm

3

So,

{\mathfrak{\red{The \: area \: of \: cuboid \: is \: 160 {cm}^{3} .}}}Theareaofcuboidis160cm

3

.

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