Question

if length, breath and height of a cuboid are in ratio 5:3.2 find volume if its total Surface area is 279cm²​

Answer 1

Answer:

The volume of a cuboid ≈ 285.84 cm³

Step-by-step explanation:

Given:

• Length, breath and height of a cuboid are in ratio 5:3.2.
• Total Surface area of a cuboid = 279 cm²

To find:

• The volume of a cuboid.

Solution:

Let the length, breadth and height of a cuboid are 5x, 3x and 2x respectively.

✰ Total Surface area of a cuboid = 2( lb + bh + hl )

Where,

l is the length of a cuboid.

b is the breadth of a cuboid.

h is the height of a cuboid.

Putting the values in the formula, we have:

• 279 = 2(( 5x × 3x ) + ( 3x × 2x ) + ( 2x × 5x ))
• 279 = 2( 15x² + 6x² + 10x² )
• 279 = 2 × 31x²
• 279 = 62x²
• x² = 279/62
• x² = 4.5
• x = √4.5
• x = 2.12 cm

Now, find out the length, breadth and height of a cuboid.

⟹ Length of a cuboid = 5 × 2.12

⟹ Length of a cuboid = 10.6 cm

⟹ Breadth of a cuboid = 3 × 2.12

⟹ Breadth of a cuboid = 6.36 cm

⟹ Height of a cuboid = 2 × 2.12

⟹ Height of a cuboid = 4.24 cm

Finally,

✰ Volume of a cuboid = l × b × h

Where,

l is the length of a cuboid.

b is the breadth of a cuboid.

h is the height of a cuboid.

Putting the values in the formula, we have:

• Volume of a cuboid = 10.6 × 6.36 × 4.24
• Volume of a cuboid ≈ 285.84 cm³

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