Question

two cubes of volume 64cm² each ae joined end to end find the surface area of the resulting cuboid​

Answer 1

AnSweR :

It is said that two cubes each of volume 64 cm³ are joined end to end. So , we have to find out surface area of the resulting cuboid.

What we have to do ?

First we will find out the side of the given cube by applying the formula of Volume of cube and then after getting the side we will have the dimensions of the resulting cuboid i.e, height and breadth will remain the same as of the side of the cube and length will going to be it's double. Thereafter , we will be using the formula for finding surface area of cuboid.

Formula need to know :

⠀⠀⠀⠀⠀⠀${\bullet \: {\boxed{\bf{Volume \: of \: Cube = Side^{3}}}}}$

⠀⠀⠀⠀⠀⠀${\bullet \: {\boxed{\bf{Surface \: Area \: of \: Cuboid = 2 (lb + bh + hl)}}}}$

Where,

l = Length of the Cuboid

B = Breadth of the Cuboid

H = Height of the Cuboid

Working Plot :

Let us we consider the unknown side of the cube be 'x' cm.

Then,

$\rightarrow{\boxed{\sf {Volume \: of \: cube \: = Side^{3}}}}$

As from given ;

• Volume → 64 cm³

$\dashrightarrow\:\:\sf 64 = (x)^{3}$

$\dashrightarrow\:\:\sf 64 = x^{3}$

$\dashrightarrow\:\:\sf \sqrt 4 \times 4 \times 4 = x$

$\dashrightarrow\:\:\sf 4 = x$

Then ,

Measurements of cuboid :

• Length will be :
• → 4 + 4 = 8cm

• → Breadth of Cuboid = 4cm

• → Height = 4cm

Now,

For the Total surface area :

$\dashrightarrow\:\:\sf T.S.A = 2(lb + bl + lh)$

$:\implies \sf T.S.A = 2[ (8 \times 4) + (4 \times 4) + (4 \times 8) ]$

$:\implies \sf T.S.A = 2(32 + 16 + 32)$

$:\implies \sf T.S.A = 2(48 + 32)$

$:\implies \sf T.S.A = 2 \times 80$

$:\implies \sf T.S.A = 160 \: cm^{2}$

$\dashrightarrow\:\: \underline{ \boxed{\sf T.S.A = 160 \: cm^{2}}}$

Therefore, the Total surface area of cuboid is 160 cm².

Answer 2

Given : Two cubes of volume 64cm² each are joined end to end together.

Need To Find : Total Surface Area of new formed Cuboid.

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❍ Finding Side of Cube to find Dimensions of Cuboid :

$\dag\:\frak{\underline {As,\:We\:know\:that\::}}$

$\dag\:\:\boxed {\sf{ Volume _{(Cube)} =\bigg( a \times a \times a \:or\:a^3 \bigg) }}$

Where,

• a is the Side of the Cube .

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ a^3 = 64}\\\\:\implies \sf{ a = \sqrt [3]{64}}\\\\:\bf{a = 4 cm }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Side \:of\:Cube\:is\:\bf{4\: cm}}}}$

⠀⠀⠀⠀Finding out Dimensions of Cuboid :

⠀⠀⠀⠀If we join two cubes together there length will be doubled of the side of a cube , Breadth & Height of new formed Cuboid will be same as the side of a cube .

• Length of Cuboid is = 2(4) = 8 cm ⠀⠀⠀⠀⠀⠀⠀⠀[ Length will be doubled]
• Breadth of Cuboid is = 4 cm ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[ Height will remain same ]
• Height of Cuboid is = 4 cm ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[ Breadth will remain same ]

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⠀⠀⠀⠀⠀⠀⠀⠀Finding Total Surface Area of New Formed Cuboid :

$\dag\:\frak{\underline {As,\:We\:know\:that\::}}$

$\dag\:\:\boxed {\sf{ Total\:Surface\:Area\:_{(Cuboid)} =\bigg( 2 ( lb + bh + hl \bigg) }}$

Where,

• l is the Length of Cuboid, b is the Breadth of Cuboid & h is the Height of Cuboid.

⠀⠀⠀⠀⠀⠀$\underline {\sf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf { T.S.A = 2( 8 \times 4 + 4 \times 4 + 4 \times 8 }\\\\:\implies \sf { T.S.A = 2( 32 + 26 + 32 }\\\\:\implies \sf { T.S.A = 2( 48 + 32 }\\\\:\implies \sf { T.S.A = 2( 80 }\\\\\underline {\boxed{\purple{ \cal {  T.S.A = \: 160cm^2}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence \:Total \:Surface \:Area\:of\:Cuboid \:is\:\bf{160\: cm^2}}}}$

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