Question

If the length, breadth and height of a cuboid are in the ratio 6:5:4 and its total surface area is 33,000 sq. m, find the dimensions of cuboid.​

Answer 1

☆ Solution ☆

Given :-

• The length, breadth and height of a cuboid are in the ratio 6:5:4 and its total surface area is 33,000 sq. m.

To Find :-

• The dimensions of cuboid.

Step-by-Step-Explaination :-

Let ,

• The length be 6x
• The breadth be 5x
• The height be 4x

Total surface area of cuboid = 2 ( lb + bh + hl )

33000 = 2 ( 6x × 5x + 5x × 4x + 4x + 6x )

33000 = 2 ( 30x² + 20x² + 24x² )

33000 = 2 ( 74x² )

33000 = 74x²

x² = 16500/74

x² ≈ 223

x ≈ 15

Now,

Dimension of Length = 6x = 6 × 15 = 90 m

Dimension of Breadth = 5x = 5 × 15 = 75m

Dimension of Height = 4x = 4 × 15 = 60m