Question

find the total surface area and latural surface area of cuboid with length breadth and the height of 20cm 12 cm and 10cm with equation​

Answer 1

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To find :-

• Total surface area of the cuboid
• Lateral surface area of the cuboid

Firstly , we will find out the lateral surface area of the cuboid

• Length ( l )= 20 centimeters
• Breadth ( b )= 12centimeters
• Height ( h )= 10centimeters

➪ Lateral surface area of cuboid = 2height(Length + breadth)

➪ Lateral surface area of cuboid = 2 × 10(20 + 12)

➪ Lateral surface area of cuboid = 2 × 10(20 + 12)

➪ Lateral surface area of cuboid = 2 × 10(32)

➪ Lateral surface area of cuboid = 20 × 32

➪ Lateral surface area of cuboid = 640cm²

∴ the lateral surface area of the cuboid is 640cm²

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Now ,we will find out the Total surface area of the cuboid

• Length ( l )= 20 centimeters
• Breadth ( b )= 12centimeters
• Height ( h )= 10centimeters

➪ Total surface area of cuboid = 2 (l x b + b x h + L x h)

➪ Total surface area of cuboid = 2 (20 x 12 + 12 x 10 + 20 x 10)cm²

➪ Total surface area of cuboid = 2 (240 + 120 + 200)cm²

➪ Total surface area of cuboid = 2 × 560 cm²

➪ Total surface area of cuboid = 1120 cm ²

∴ the Total surface area of cuboid is 1120cm²

Answer 2

Given : Length, breadth and height of a cuboid are 20cm , 12cm and 10cm respectively.

To Find : L.S.A and T.S.A of the cuboid.

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Here

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• Length of the cuboid = 20cm
• Breadth of the cuboid = 12cm
• Height of the cuboid = 10cm

$\: \:$

Firstly, we'll find the L.S.A of the cuboid.

$\: \:$

❍ As we know that

$\: \:$

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

$\:$

Put the values in the formula and solve.

$\: \:$

$\sf:\implies \: L.S.A_{(cuboid)} = 2(10)(20 + 12) \\ \\ \\ \sf:\implies \: L.S.A_{(cuboid)} = 20(10 + 12) \\ \\ \\ \sf:\implies \: L.S.A_{(cuboid)} = 20 \times 32 \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{L.S.A_{(cuboid)} = 640 \: {cm}^{2} }}} \: \bigstar \:$

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Now, we'll find the T.S.A of the cuboid.

$\: \:$

❍ As we know that

$\: \:$

$\star \: \: \underline{\boxed{\sf\pink{T.S.A_{(cuboid)} = 2(lb + bh + lh)}}} \:$

$\:$

Put the values in the formula and solve.

$\: \:$

$\sf:\implies \: T.S.A_{(cuboid)} = 2[(20 \times 12) + (12 \times 10) + (20 \times 10)] \\ \\ \\ \sf:\implies \: T.S.A_{(cuboid)} = 2[240 + 120 + 200] \\ \\ \\ \sf:\implies \: T.S.A_{(cuboid)} = 2 \times 560 \\ \\ \\\sf:\implies \underline{\boxed{\mathfrak\purple{T.S.A_{(cuboid)} = 1120 \: cm {}^{2} }}} \: \bigstar \\ \\ \\ \\ \sf \therefore{\underline{Hence ,\: the \: L.S.A\: and \:T.S.A \: of \: the \: cuboid \: are \: \bold{440 {cm}^{2}} \: and \: \bold{1120 \: {cm}^{2} \: }respectively. }}$