Question

the length, breadth and height of a cuboid are in ratio 5:3:2 and its total surface area is 3968cm2.find the dimensions of the cuboid​

Answer 1

Answer :

• Length of the cuboid = 40 cm
• Breadth of the cuboid = 24 cm
• Height of the cuboid = 16 cm

Explanation :-

Given :-

• Ratio of the length, breadth and height of the cuboid = 5 : 3 : 2
• Total surface area of cuboid = 3968 cm²

To find :-

• Dimensions of the cuboid

Knowledge Required :-

→ Formula of total surface area of cuboid :-

• TSA = 2(lb + bh + hl)

where,

• l = length of the cuboid
• b = breadth of the cuboid
• h = height of the cuboid

Solution :-

Let,

• length of the cuboid = 5x
• Breadth of the cuboid = 3x
• Height of the cuboid = 2x

Using the formula of TSA of cuboid,

⇒ TSA = 2(lb + bh + hl)

⇒ 3968 = 2(5x × 3x + 3x × 2x + 2x × 5x)

⇒ 3968 = 2(15x² + 6x² + 10x²)

⇒ 3968/2 = 15x² + 6x² + 10x²

⇒ 1984 = 31x²

⇒ 1984/31 = x²

⇒ 64 = x²

⇒ Taking square root on both the sides

⇒ √64 = x

⇒ ± 8 Reject - ve = x

⇒ 8 = x

The value of x = 8

Substitute the value of x in the dimensions of cuboid which we've let.

→ Length of the cuboid = 5x = 5 × 8 = 40 cm

→ Breadth of the cuboid = 3x = 3 × 8 = 24 cm

→ Height of the cuboid = 2x = 2 × 8 = 16 cm

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Let's verify :-

Substitute the value of x in 3968 = 2(5x × 3x + 3x × 2x + 2x × 5x)

LHS = 3968

Taking RHS,

⇒ 2(5x × 3x + 3x × 2x + 2x × 5x)

⇒ 2(15x² + 6x² + 10x²)

⇒ 2(31x²)

⇒ 2(31 × (8)²)

⇒ 2(31 × 64)

⇒ 3968

RHS = 3968

LHS = RHS

Hence, verified.

Answer 2

Given :-

• Ratio of the length, breadth and height of the cuboid = 5 : 3 : 2
• Total surface area of cuboid = 3968 cm²

To Find :-

• Dimensions of Cuboid

Solution :-

➞ Let Length of the cuboid = 5x

➞ Let Breadth of the cuboid = 3x

➞ Let Height of the cuboid = 2x

According to the Question :

• TSA = 2(lb + bh + hl)
• 3968 = 2(5x × 3x + 3x × 2x + 2x × 5x)
• 3968 = 2(15x² + 6x² + 10x²)
• 3968/2 = 15x² + 6x² + 10x²
• 1984 = 31x²
• 1984/31 = x²
• 64 = x²
• √64 = x
• 8 = x

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Verification :

• TSA = 2(lb + bh + hl)
• TSA = 2(5x × 3x + 3x × 2x + 2x × 5x)
• TSA = 2(15x² + 6x² + 10x²)
• TSA = 2(31x²)
• TSA = 2(31 × (8)²)
• TSA = 2(31 × 64)
• 3968 = 3968

Hence verified.

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Therefore :

• Length = 5x = 5 × 8 = 40cm
• Breadth = 3x = 3 × 8 = 24cm
• Height = 2x = 2 × 8 = 16cm

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