Question

The length breath and height
of cuboid are in the ratio 5:4:2
if the T.S.A is 1216cm².
Find volume of cuboid​​

Answer 1

Given information,

The length, breath and height of cuboid are in the ratio 5:4:2. If the T.S.A is 1216 cm². Find volume of cuboid.

• Ratio of L, B and H = 5:4:2
• T.S.A of cuboid = 1216 cm²

Let,

• L, B and H = 5x, 4x, and 2x.

Using formula,

✪ T.S.A of cuboid = 2(LB + BH + HL) ✪

Where,

• L denotes length of cuboid
• B denotes breadth of cuboid
• H denotes height of cuboid

We have,

• L = 5x
• B = 4x
• H = 2x
• T.S.A = 1216 cm²

Putting all values,

➻ 1216 = 2[(5x)(4x) + (4x)(2x) + (2x)(5x)]

➻ 1216 = 2(20x² + 8x² + 10x²)

➻ 1216 = 2(38x²)

➻ 1216 = 2 × 38x²

➻ 1216 = 76x²

➻ x² = 1216/76

➻ x² = 16

➻ x = √16

➻ x = √(4 × 4)

➻ x = 4

Now,

◔ Length of cuboid = 5x

◔ Length of cuboid = 5 × 4

◔ Length of cuboid = 20 cm

And,

◔ Breadth of cuboid = 4x

◔ Breadth of cuboid = 4 × 4

◔ Breadth of cuboid = 16 cm

Also,

◔ Height of cuboid = 2x

◔ Height of cuboid = 2 × 4

◔ Height of cuboid = 8 cm

• Henceforth, dimensions of cuboid (length, breadth and height) are 20 cm, 16 cm and 8 cm.

★ Finding volume of cuboid ::

Using formula,

✪ Volume of cuboid = LBH ✪

Where,

• L denotes length of cuboid
• B denotes breadth of cuboid
• H denotes height of cuboid

We have,

• L = 20 cm
• B = 16 cm
• H = 8 cm

Putting all values,

➻ Volume of cuboid = (20)(16)(8)

➻ Volume of cuboid = 20 × 16 × 8

➻ Volume of cuboid = 2560 cm³

• Henceforth, volume of cuboid is 2560 cm³.

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Answer 2

✿Answer:-

Given length , breadth and height of cuboid are in ratio 5:4:3

Let length , breadth and height of cuboid are 5a,4a and 2a respectively

Then surface area of cuboid =

=2(5a×4a+4a×2a+5a×2a)

$2(20a {}^{2} + 8a {}^{2} + 10a {}^{2}) = 76a {}^{2} sq.cm$

But surface area is given 1216 sq. cm

Therefore,

$76a {}^{2} = 1216 = a {}^{2} = 16 = a = 4$

Then the sides of cuboid is 20 cm ,16 cm and 8 cm

Then volume of cuboid =

=20×16×8 cubic cm

= 2560 cubic cm