Question

find the total ( as per answer given ) surface area of closed , cardboard box of length 40 cm , breadth 30 cm and height 10 cm​

Answer 1

$\sf Given \begin{cases} & \sf{Length\:of\:cardboard\:box = \bf{40\;cm}} \\ & \sf{Breadth\:of\: cardboard\:box = \bf{30\:cm}} \\ & \sf{Height\:of\:cuboidal\:box = \bf{10\:cm}} \end{cases}$

To find: Total surface area of closed cardboard box?

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DIAGRAM:

$\setlength{\unitlength}{0.74 cm}\begin{picture}(0,0)\thicklines\put(3.5,6.1){\sf 30\:cm}\put(7.7,6.3){\sf 40\:cm}\put(11.3,7.45){\sf 10\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Total\:surface\:Area_{\;(cuboid)} = 2(lb + bh + hl)}}}}$

$\bf{\dag}\;{\underline{\frak{Substituting\:the\:given\:values,}}}\\ \\ \\:\implies\sf 2(40 \times 30 + 30 \times 10 + 10 \times 40)\\ \\ \\ :\implies\sf 2(1200 + 300 + 400)\\ \\ \\ :\implies\sf 2(1900)\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{3800\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Total\:surface\:area\:of\:cuboid\:is\: \bf{3800\:cm^2}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• $\sf Volume\:of\:cuboid = l \times b \times h$

• $\sf Total\:surface\:area\:of\:cuboid = 2(lb + bh + hl)$

• $\sf Curved\:surface\:area\:of\:cuboid = 2(l + b)h$

• $\sf Diagonal\:of\:cuboid = \sqrt{l^2 + b^2 + h^2}$

Answer 2

Answer:

Given :-

• A closed cardboard box whose length is 40 cm, breadth is 30 cm and height is 10 cm.

To Find :-

• What is the total surface area of closed cardboard box.

Formula Used :-

$\boxed{\bold{\small{T.S.A\: of\: Cuboid\: =\: 2(LB + BH + HL)}}}$

where,

• T.S.A = Total surface area
• L = Length
• B = Breadth
• H = Height

Solution :-

Given :

• Length = 40 cm
• Breadth = 30 cm
• Height = 10 cm

According to the question by using the formula we get,

⇒ $\sf T.S.A\: =\: 2(40 \times 30) + (30 \times 10) + (10 \times 40)$

⇒ $\sf T.S.A\: =\: 2(1200 + 300 + 400)$

⇒ $\sf T.S.A\: =\: 2(1900)$

⇒ $\sf T.S.A\: =\: 2 \times 1900$

➠ $\sf\red{T.S.A\: =\: 3800\: {cm}^{2}}$

$\therefore$ The total surface area of closed cardboard box is 3800 cm² .