Question

The dimensions of a cuboid are in the ratio of 2:3:4 and its total surface area is 280m^2. Find the dimensions.​

Answer 1

Given -

• Dimensions of cuboid = 2 : 3 : 4

• Total surface area of cuboid = 280m²

To find -

• The dimensions.

Formula used -

• TSA of cuboid = 2(lb + bh + hl)

Solution -

In the question, we are provided with the ratio of a cuboid and total surface area of the is 280m², first we will give every constant a name x, and then we will apply the formula of total surface area of cuboid, after that, we will place the obtained value in place of x, that will give us the dimensions of the cuboid.

According to question -

Length of cuboid = 2x

Breadth of cuboid = 3x

Height of cuboid = 4x

Total surface area of cuboid = 280m²

On substituting the values -

$\sf \: surface \: area \: = 2(lb \: + \: bh + \: hl) \\ \\ \sf \: 280 {m}^{2} \: = 2(2x)(3x) \: + \: (3x)(4x) \: + (4x)(2x) \\ \\ \sf \: 280 {m}^{2} \: = 2(6x^{2} \: + 12x^{2} \: + 8x^{2}) \\ \\ \sf \: 280 {m}^{2} \: = 2(26x^{2}) \\ \\ \sf \: 280 {m}^{2} \: = 52x^{2} \\ \\ \sf \: x^{2} \: = \dfrac{280}{52} \\ \\ \sf x^{2} \: = 5.3m \\ \\ \sf x^{2} = \sqrt{5.3} \\ \\ \sf x = 2.3m$

Now -

We will find the values of each dimensions, by multiplying 2.3, with length, breadth and height.

Length = 2x = 2 × 2.3 = 4.6m

Breadth = 3x = 3 × 2.3 = 6.9m

Height = 4x = 4 × 2.3 = 9.2m

2 more formulae of cuboid -

1. Lateral surface area = 2h(l + b)

2. Volume = L × B × H

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Answer 2

Answer:

Given :-

• Ratio of length Breadth and height of cuboid = 2:3:4
• TSA = 280 m²

To Find :-

Dimensions

Solution :-

We know that

TSA = 2(lb + bh + lh)

280 = 2(2x × 3x + 3x × 4x + 2x × 4x)

280 = 2(6x² + 12x² + 8x²)

280 = 2(26x²)

280 = 52x²

280/52 = x²

√5.3 = x

2.3 = x

Therefore,

Length = 2x = 2 × 2.3 = 4.6 m

Breadth = 3x = 3 × 2.3 = 6.9 m

Height = 4x = 4 × 2.3 = 9.2 m