Question

Two identical cubes each of T.S.A = 6 sq.cm. are joined end to end . Which of the following is the T.S.A of the cuboid so formed
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Answer 1

GivEn:-

• T.S.A . of two identical cubes = 6 cm²

To find:-

• T.S.A. of cuboid formed

SoluTion:-

$\dag\;{\underline{\underline{\bf{\blue{According\;to\;question:-}}}}}$

☯ Total Surface area of cube = 6 cm²

$:\implies$ 6a² = 6 cm²

$:\implies\sf a^2 = \cancel{ \dfrac{6}{6}}$

$:\implies$ a² = 1

$\small\sf\;\;\star\;{\underline{Taking\;Sqrt.\;both\;sides:-}}$

$:\implies {\underline{\underline{\bf{\pink{a = 1}}}}}$ ★

GivEn that,

✩ 2 cubes are joined to form a cuboid,

Therefore,

• Length of cuboid = 2

• Breadth of cuboid = 1

• Height of cuboid = 1

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${\underline{\underline{\bf{\red{\DIAGRAM:}}}}}$

⋆ CUBE:

$\setlength{\unitlength}{0.65cm}\begin{picture}(2,3)\thicklines\put(2,6){\line(1,0){3.3}}\put(2,9){\line(1,0){3.3}}\put(5.3,9){\line(0,-1){3}}\put(2,6){\line(0,1){3}}\put(0,7.3){\line(1,0){3.3}}\put(0,10.3){\line(1,0){3.3}}\put(0,10.3){\line(0,-1){3}}\put(3.3,7.3){\line(0,1){3}}\put(2,6){\line(-3,2){2}}\put(2,9){\line(-3,2){2}}\put(5.3,9){\line(-3,2){2}}\put(5.3,6){\line(-3,2){2}}\put(3.4,5.5){\sf1 cm}\put(0,6.3){\sf1 cm}\put(5.5,7.5){\sf1 cm}\end{picture}$

⋆ CUBOID Formed by joining 2 cubes:

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{2 cm}}\put(4,6.3){\sf{1 cm}}\put(10,7.5){\sf{1 cm}}\end{picture}$

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☯ Total Surface Area of cuboid = 2(lb + bh + hl)

$:\implies$ 2(2 × 1 + 1 × 1 + 1 × 2)

$:\implies$ 2(2 + 1 + 2)

$:\implies$ 2(5)

$:\implies {\underline{\underline{\bf{\pink{10\;cm^2}}}}}$ ★

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