Question

Calculate the surface area of a cuboid whose length is 8cm width is 5cm and hight is 6cm.

Answer 1

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

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

⋆ Length of cuboid is 8 centimetres

⋆ Breadth of cuboid is 5 centimetres

⋆ Height of cuboid is 6 centimetres

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

⋆ Surface area of cuboid

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

⋆ Surface area of cuboid = 236 cm²

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

⋆ Surface area of cuboid formula

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

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

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

⋆ Structure of a cuboid:

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

${\bigstar \:{\pmb{\sf{\underline{Some \: formulas \: regard \: cuboid...}}}}}$

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

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

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

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

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

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

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

${\sf{:\implies Surface \: area \: of \: cuboid \: = 2(8 \times 5 + 5 \times 6 + 8 \times 6)}}$

${\sf{:\implies Surface \: area \: of \: cuboid \: = 2(40 + 30 + 48)}}$

${\sf{:\implies Surface \: area \: of \: cuboid \: = 2(70 + 48)}}$

${\sf{:\implies Surface \: area \: of \: cuboid \: = 2(118)}}$

${\sf{:\implies Surface \: area \: of \: cuboid \: = 236 \: cm \: sq.}}$

• Henceforth, 236 cm sq. is surface area of the cuboid.