Question

27. Find the total surface area and lateral surface area of a shoe box whose length, breath, and height are 30CM, 25CM and 15 cm respectively.​

Answer 1

$\underline{ \sf \large{Solution-} }$

Here it is given that,

• Length of shoe box (l) = 30 cm
• Breadth of shoe box (b) = 25 cm
• Height of shoe box (h) = 15 cm

Now,

➢ Total surface area = 2(lb+bh+lh)

$\tt \implies 2(30\times25 +25 \times 15+30\times15)$

$\tt \implies 2(750 +375+450)$

$\tt \implies 2(1575) = \boxed{ \tt \red {3150 \: cm^{2} }}$

∴ Total surface area = 3150 cm²

Now,

➢ Lateral surface area = 2h(l+b)

$\tt \implies 2h(l+b)$

$\tt \implies 2 \times 15(30+25)$

$\tt \implies 30(55) = \boxed{ \tt \red{1650 \: cm^{2} }}$

∴ Lateral surface area = 1650 cm²

Answer 2

Answer:

Given :-

• A shoe box whose length, breadth and height are 30 cm, 25 cm and 15 cm respectively.

To Find :-

• What is the total surface area and lateral surface area of a shoe box.

Formula Used :-

$\clubsuit$ Total Surface Area or T.S.A. Of Cuboid Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Total\: Surface\: Area_{(Cuboid)} =\: 2(lb + bh + hl)}}}\: \: \: \bigstar$

where,

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

$\clubsuit$ Lateral Surface Area or L.S.A. Of Cuboid Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Lateral\: Surface\: Area_{(Cuboid)} =\: 2 \times (l + b) \times h}}}\: \: \: \bigstar$

where,

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

Solution :-

❒ In case of total surface area of a shoe box :

Given :

• Length = 30 cm
• Breadth = 25 cm
• Height = 15 cm

According to the question by using the formula we get,

$\small \implies \bf T.S.A._{(Shoe\: Box)} =\: 2(lb + bh + hl)$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2\bigg\{(30 \times 25) + (25 \times 15) + (15 \times 30)\bigg\}$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2\bigg\{(750) + (375) + (450)\bigg\}$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2\bigg\{750 + 375 + 450\bigg\}$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2\bigg\{1125 + 450\bigg\}$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2\bigg\{1575\bigg\}$

$\small \implies \sf T.S.A._{(Shoe\: Box)} =\: 2 \times 1575$

$\small \implies \sf\bold{\red{T.S.A._{(Shoe\: Box)} =\: 3150\: cm^2}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: total\: surface\: area\: or\: T.S.A.\: of\: shoe\: box\: is\: 3150\: cm^2\: .}}}$

❒ In case of lateral surface area of a shoe box :

Given :

• Length = 30 cm
• Breadth = 25 cm
• Height = 15 cm

According to the question by using the formula we get,

$\dashrightarrow \bf L.S.A._{(Shoe\: Box)} =\: 2 \times (l + b) \times h$

$\dashrightarrow \sf L.S.A._{(Shoe\: Box)} =\: 2 \times (30 + 25) \times 15$

$\dashrightarrow \sf L.S.A._{(Shoe\: Box)} =\: 2 \times (55) \times 15$

$\dashrightarrow \sf L.S.A._{(Shoe\: Box)} =\: 2 \times 55 \times 15$

$\dashrightarrow \sf L.S.A._{(Shoe\: Box)} =\: 110 \times 15$

$\dashrightarrow \sf\bold{\red{L.S.A._{(Shoe\: Box)} =\: 1650\: cm^2}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: lateral\: surface\: area\: or\: L.S.A.\: of\: shoe\: box\: is\: 1650\: cm^2\: .}}}$

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