Question

The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 88m.find the dimensions.​

Answer 1

Correct Question:

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The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 88m$^{2}$. Find the dimensions.

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Given:

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• Dimensions of cuboid are given in the ratio of 1 : 2 : 3.
• Total surface area of the cuboid = 88 m$^{2}$

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To find:

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Dimensions of the cuboid.

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Solution:

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Let the dimensions be x, 2x and 3x in metres.

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We know that,

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

So,

$\implies$ 2(x × 2x + 2x × 3x + x × 3x) = 88

$\implies$ 2(2x$^{2}$ + 6x$^{2}$ + 3x$^{2}$) = 88

$\implies$ 2 × 11x$^{2}$ = 88

$\implies$ 22x$^{2}$ = 88

$\implies$ x$^{2}$ = 4

$\implies$ x$^{2}$ = 2$^{2}$

$\implies$ x = 2 m

Now, its dimension = 2x = 2 × 2 = 4

3x = 3 × 2 = 6.

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Thus, the dimensions of the cuboid are 2 m, 4 m and 6 m respectively.

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More formulas:

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For cuboid:

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

Lateral surface area of the cuboid = 2(l + b)h

Diagonal of the cuboid

$= \sqrt{l {}^{2} + b {}^{2} + h {}^{2} }$

Length of all 12 edges of the cuboid = 4(l + b + h)

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For cube:

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Total surface area of the cube = 6l$^{2}$

Lateral surface area of the cube = 4l$^{2}$

Diagonal of the cube

$= \sqrt{3} \: l$

Length of all 12 edges of the cube = 12 l

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Answer 2

Correct Question:

The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is 88m².Find the dimensions.

Given:

Ratio of Dimensions of 1 : 2 : 3.

T.S.A of the cuboid = 88 m²

To find :-

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What is the Dimensions of the cuboid ?

Solution:

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Consider the dimensions be x, 2x and 3x in metres.

Applying the formula :-

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

Substituting the values in the above formula :-

2(x × 2x + 2x × 3x + x × 3x) = 88

2(2x$^{2}$ + 6x$^{2}$ + 3x$^{2}$) = 88

2 × 11x$^{2}$ = 88

22x$^{2}$ = 88

x$^{2}$ = 4

x$^{2}$ = 2$^{2}$

= x = 2 m

Therefore ,

Dimension

= 2x = 2 × 2 = 4

3x = 3 × 2 = 6.

So the dimensions are :- ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

2 m, 4 m and 6 m .

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Additional Information :

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height.

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

❥ Lateral surface area of the cuboid = 2(l + b)h

❥ Length of all 12 edges of the cuboid = 4(l + b + h)⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

❥Lateral surface area of the cuboid = 2(l + b)h

❥ Diagonal of the cuboid = { l²+ b²+ h²}

❥ Length of all 12 edges of the cuboid = 4(l + b + h)

❥Total surface area of the cube = 6l$^{2}$

❥Lateral surface area of the cube = 4l$^{2}$

❥Diagonal of the cube

$= \sqrt{3} \: l$

❥ Length of all 12 edges of the cube = 12 l

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