Question

Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid.

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Answer 1

Answer:

when two cubes are joined length will be doubled.

so,length=6+6=12 cm

breadth and height doesn't changes.

so,breadth=6cm

height=6cm

total surface area=2(lb+bh+lh)

=2(12×6+6×6+12×6)

=2(72+36+72)

=2(180)

=360 cubic cm

Answer 2

$\star \; {\underline{\boxed{\orange{\pmb{\textbf{\textsf{ Given \; :- }}}}}}}$

• Edge of the Cubes = 6 cm

$\star \; {\underline{\boxed{\purple{\pmb{\textbf{\textsf{ To \; Find \; :- }}}}}}}$

• Total Surface Area of the Cuboid = ?

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$\star \; {\underline{\boxed{\red{\pmb{\textbf{\textsf{ SolutioN \; :- }}}}}}}$

$\dag \; {\underline{\underline{\sf{ \; As \; we \; Know \; That \; :- }}}}$

• ${\underline{\boxed{\pmb{\sf{ TSA{\small_{(Cuboid)}} = 2 ( lb + bh + hl ) }}}}}$

Where :

• l = Length
• b = Breadth
• h = Height

$\dag \; {\underline{\underline{\sf{ \; Now, \; We \; Have \; :- }}}}$

$\longmapsto$ By placing the two Cubes together .We can get :-

• Length = 6 + 6 = ${\color{darkblue}{\sf{ 12 \; cm }}}$
• Breadth = ${\color{darkblue}{\sf{ 6 \; cm }}}$
• Height = ${\color{darkblue}{\sf{ 6 \; cm }}}$

$\dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Surface \; Area \; :- }}}}$

$\begin{gathered} \qquad \; \pink\dashrightarrow \; \; {\purple{\sf{ TSA = 2 \bigg[ \bigg( l \times b \bigg) + \bigg( b \times h \bigg) + \bigg( h \times l \bigg) \bigg] }}} \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { TSA = 2 \bigg[ \bigg( 12 \times 6 \bigg) + \bigg( 6 \times 6 \bigg) + \bigg( 6 \times 12 \bigg) \bigg] } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { TSA = 2 \bigg( 72 + 36 + 72 \bigg) } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { TSA = 2 \bigg( 108 + 72 \bigg) } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { TSA = 2 \times 180 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\red{\pmb{\frak { Total \; Surface \; Area = 360 \; {cm}^{2} }}}}}} \; \bigstar \\ \\ \\ \\ \end{gathered}$

$\therefore \;$ Total Surface Area of the resulting Cuboid is 360 cm² .

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