Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 176 m². Find the
dimensions.​

Answer 1

let the dimensions be 1y, 2y, 3y

TSA of cuboid= 2×(lb+bh+lh)

176= 2(1y×2y+2y×3y+3y×1y)

176/2= 2y+6y+3y

88= 11y

88/11= y

8=y

hence the dimensions are-

1y= 1×8= 8m

2y= 2×8= 16m

3y= 3×8 = 24m

Hope this helps.

Answer 2

Given :

• The dimensions of a cuboid are in the ratio 1:2:3.
• It's total surface area is 176 m².

To find :

• The dimensions =?

Formula Used :

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

Step-by-step explanation :

It is Given that,

It's total surface area is 176 m².

Let, the dimensions of a cuboid are in the ratio 1x, 2x and 3x.

As We know that,

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

Substituting the values in the above formula, we get,

176 m² = 2(1x × 2x + 2x × 3x + 3x × 1x)

176 m² = 2(2x² + 6x² + 3x²)

.

176 m² = 2(11x²)

22x² = 176 m²

x² = 176 m²/22

x² = 8 m²

x = 8 m

Therefore, We got the value of, x = 8 m.

Hence,

1x, 1 × 8 = 8 m.

2x, 2 × 8 = 16 m.

3x, 3 × 8 = 24 m.

Therefore, The dimensions of a cuboid are 8 m, 16 m and 24 m respectively.