Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is

352cm2

. Find the dimensions.​

Answer 1

Step-by-step explanation:

Let the length of the cuboid =x, breadth =2x, height =3x

Total surface area of a cuboid =2(l×b+b×h+l×h)

Given, total surface area of the cuboid =88m

2

⇒2(x×2x+2x×3x+x×3x)=88m

2

⇒22x

2

=88

⇒x=2

Hence, the length of the cuboid =x=2m, breadth =2x=4m, height =3x=6m

Answer 2

Given:

• Dimensions are in the ratio 1:2:3
• TSA = 352 cm²

To find:

1. Dimensions = ?

Solution:

Consider the sides are x, 2x and 3x

• Length = x
• Breadth = 2x
• Height = 3x

TSA of cuboid = 2(lb + bh + hl)

⇒ TSA = 2(x.2x + 2x.3x + 3x.x)

⇒ 352 = 2(2x² + 6x² + 3x²)

⇒ 352 = 2(11x²)

⇒ 352 = 22x²

⇒ 22x² = 352

⇒ x² = 352 ÷ 22

⇒ x² = 16

⇒ x = √16

⇒ x = ±4

Dimensions cannot be negative.

∴ x = 4 cm

Now, for finding the dimensions,

• Length = x = 4 cm

• Breadth = 2x = 2(4) = 8 cm

• Height = 3x = 3(4) = 12 cm

Therefore,

★ Length = 4 cm

★ Breadth = 8 cm

★ Height = 12 cm