Question

three identical cubes of side 4 cm are joined end to end. find the total surface area and lateral surface area of the new resulting cuboid​

Answer 1

GiveN :

• Three cubes of side 4cm are joined end to end.

To FinD :

• Total Surface Area and Curved Surface Area of the new resulting cuboid.

SolutioN :

If three cubes each of side 4cm are joined end to end to make a cuboid. Then new dimensions will be :

• Length = 3(4) = 12 cm
• Breadth = 4 cm
• Height = 4 cm

Now, use formula for CSA of cuboid :

$\implies$ C.S.A = 2(length + Breadth) * Height

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$\implies$ C.S.A = 2(12 + 4)4

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$\implies$ C.S.A = 2(16)4

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$\implies$ C.SA = 32*4

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$\implies$ C.S.A = 128

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$\small{\underline{\rm{\therefore \:C.S.A \: of \: Cuboid \: is \: 128 \: cm^2}}}$

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Now, use formula for Total Surface Area of cuboid :

$\implies$ T.S.A = 2(lb + bh + hl)

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$\implies$ T.S.A = 2(12*4 + 4*4 + 12*4)

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$\implies$ T.S.A = 2(48 + 16 + 48)

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$\implies$ T.S.A = 2(112)

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$\implies$ T.S.A = 224

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$\small \underline {\rm{\therefore \: T.S.A \: of \: Cuboid \: is \: 224 \: cm^2}}$

Answer 2

✰ AnSwer :

• CSA and TSA of cuboid are 128 cm² and 224 cm² respectively.

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✒ GiVen :

• 3 cubes of side 4 cm are joined together at their ends.

✒ To Find :

• CSA and TSA of the new resulting cuboid.

✒ SoluTion :

• It is given that 3 cubes each of side 4cm are joined together at their ends to form a cuboid.

★ Accordingly, the new dimensions will be :

• Breadth = 4 cm

• Length = 12 cm

• Height = 4 cm

☯ By using the formula of CSA of a cuboid,

➠ CSA = 2(L + B) × H

➠ CSA = 2(12 + 4)4

➠ CSA = 2(16)4

➠ CSA = 32 × 4

➠ CSA = 128 cm²

• CSA of cuboid = 128 cm²

Similarly,

☯ By using the formula of TSA of a cuboid,

➔ TSA = 2(LB + BH + HL)

➔ TSA = 2(12 × 4 + 4 × 4 + 12 × 4)

➔ TSA = 2(48 + 16 + 48)

➔ TSA = 2(64 + 48)

➔ TSA = 2(112)

➔ TSA = 224 cm²

• TSA of the cuboid = 224 cm²

Therefore, CSA and TSA of cuboid are 128 cm² and 224 cm² respectively.

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