Question

find the lateral surface area and total surface area of cuboid dimensions are 26 m,14m , 6.5 m ?​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ A cuboid is given.

⋆ Dimensions of the cuboid are 26 metres, 14 metres, 6.5 metres respectively. Henceforth,

• Length = 26 metres
• Breadth = 14 metres
• Height = 6.5 metres

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ Lateral surface area of this cuboid

⋆ Total surface area of this cuboid

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Lateral surface area of this cuboid = 520 metres sq.

⋆ Total surface area of this cuboid = 1248 metres sq.

${\bigstar \:{\pmb{\sf{\underline{Using \: concepts...}}}}}$

⋆ Formula to find out LSA of a cuboid.

⋆ Formula to find out TSA of a cuboid

${\bigstar \:{\pmb{\sf{\underline{Using \: formulas...}}}}}$

${\small{\underline{\boxed{\sf{\star \: LSA \: of \: cuboid \: = 2h(l+b)}}}}}$

${\small{\underline{\boxed{\sf{\star \: TSA \: of \: cuboid \: = 2(l \times b + b \times h + l \times h)}}}}}$

• (Where, LSA denotes lateral surface area, l denotes length, b denotes breadth, h denotes height, TSA denotes total surface area)

${\bigstar \:{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Firstly let us find TSA of cuboid.

${\small{\underline{\boxed{\sf{:\implies TSA \: of \: cuboid \: = 2(l \times b + b \times h + l \times h)}}}}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(l \times b + b \times h + l \times h)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(26 \times 14 + 14 \times 6.5 + 26 \times 6.5)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(364 + 14 \times 6.5 + 26 \times 6.5)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(364 + 91 + 26 \times 6.5)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(364 + 91 + 169)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(455 + 169}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2(624)}}$

${\sf{:\implies TSA \: of \: cuboid \: = 2 \times 624}}$

${\sf{:\implies TSA \: of \: cuboid \: = 1248 \: m^{2}}}$

${\pmb{\sf{\underline{\therefore \: TSA \: of \: cuboid \: = 1248 \: m^{2}}}}}$

~ Now let us find LSA of cuboid.

${\small{\underline{\boxed{\sf{:\implies LSA \: of \: cuboid \: = 2h(l+b)}}}}}$

${\sf{:\implies LSA \: of \: cuboid \: = 2h(l+b)}}$

${\sf{:\implies LSA \: of \: cuboid \: = 2(6.5) (26+14)}}$

${\sf{:\implies LSA \: of \: cuboid \: = 2 \times 6.5 (26+14)}}$

${\sf{:\implies LSA \: of \: cuboid \: = 13.0 (26+14)}}$

${\sf{:\implies LSA \: of \: cuboid \: = 13.0 (40)}}$

${\sf{:\implies LSA \: of \: cuboid \: = 13.0 \times 40}}$

${\sf{:\implies LSA \: of \: cuboid \: = 520 \: m^{2}}}$

${\pmb{\sf{\underline{\therefore \: LSA \: of \: cuboid \: = 520 \: m^{2}}}}}$

${\large{\pmb{\sf{\underline{Some \: Formulas...}}}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto TSA \: of \: cuboid \: = \: 2(l \times b + b \times h + l \times h)}}$

$\; \; \; \; \; \; \;{\sf{\leadsto LSA \: of \: cuboid \: = \: 2h(l+b)}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Volume \: of \: cuboid \: = \: L \times B \times H}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Diagonal \: of \: cuboid \: = \: \sqrt{3l}}}$

$\; \; \; \; \; \; \;{\sf{\leadsto Perimeter \: of \: cuboid \: = \: 12 \times Sides}}$

${\large{\pmb{\sf{\underline{StrucTure \: of \: cuboid...}}}}}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf x\:cm}\put(7.7,6.3){\sf y\:cm}\put(11.3,7.45){\sf z\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

Answer 2

${ \pink{ \underline{ \sf{ \maltese{ \pmb{ \: Given : }}}}}}$

➱ Dimensions of the cubiod

• ★ Lenght = 26m
• ★ Breadth = 14m
• ★ Hieght = 6.5m

${ \pink{ \underline{ \sf{ \maltese{ \pmb{ \: To \: Find : }}}}}}$

• The Lateral surface area of the cubiod
• The Total surface area of the cubiod

${ \pink{ \underline{ \sf{ \maltese{ \pmb{ \: Solution: }}}}}}$

We know that,

${ \blue{ \star \: { \underline{ \boxed{ \sf{ \pink{T.S.A _{(cuboid)} = 2(lb + bh + hl)}}}}}}}$

Here,

• Length = 26m
• Breath = 14m
• Hieght = 6.5m

Substituting the values,

${ : \implies} \rm \: T.S.A = 2(l b + hl + bh) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: T.S.A = 2(26 \times 14 + 6.5 \times 26 + 14 \times 6.5) \\ \\ \\ { : \implies} \rm \: T.S.A = 2(364 + 169 + 91) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: T.S.A = 2(624) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: T.S.A ={ \boxed{ \pmb{ \frak{ 1248 {cm}^{2} }}} \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the total surface area is 1248cm²

~ Now, let's find the Lateral surface area

We know that,

${ \blue{ \star \: { \underline{ \boxed{ \sf{ \pink{L.S.A _{(cuboid)} = 2h(l + b)}}}}}}}$

Here,

• Length = 26m
• Breath = 14m
• Hieght = 6.5m

Substituting we get,

${ : \implies} \rm \: L.S.A = 2h(l + b) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: L.S.A = 2 \times 6.5(26 + 14) \\ \\ \\{ : \implies} \rm \: L.S.A = 13 \times 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: L.S.A = { \boxed{ \pmb{ \frak{520 {m}^{2} }}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the lateral surface area is 520m²