Question

A cuboid has a volume of 480cm^3.The ratio of the length to width to height is 5:4:3. Find the dimensions of cuboid.​

Answer 1

Given information,

A cuboid has a volume of 480 cm³. The ratio of the length to width to height is 5:4:3. Find the dimensions of cuboid.

• Ratio of L to W to H = 5:4:3
• Volume of cuboid = 480 cm³
• Dimensions of cuboid = ?

Let,

• L, W and H = 5x, 4x, and 3x.

Using formula,

✪ Volume of cuboid = LWH ✪

Where,

• L denotes length of cuboid
• W denotes width of cuboid
• H denotes height of cuboid

We have,

• L = 5x
• W = 4x
• H = 3x
• Volume of cuboid = 480 cm³

Putting all values,

➻ 480 = (5x)(4x)(3x)

➻ 480 = 5x × 4x × 3x

➻ 480 = 60x³

➻ x³ = 480/60

➻ x³ = 48/6

➻ x³ = 8

➻ x = cube root(8)

➻ x = cube root (2 × 2 × 2)

➻ x = 2

Now,

◒ Length of cuboid = 5x

◒ Length of cuboid = 5 × 2

◒ Length of cuboid = 10 cm

And,

◒ Width of cuboid = 4x

◒ Width of cuboid = 4 × 2

◒ Width of cuboid = 8 cm

Also,

◒ Height of cuboid = 3x

◒ Height of cuboid = 3 × 2

◒ Height of cuboid = 6 cm

• Henceforth, dimensions of cuboid (length, width and height) are 10 cm, 8 cm and 6 cm.

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Answer 2

Given :

Volume of Cuboid is 480 cm²

Ratio of length to width to height is 5:4:3.

What To Find :

Dimensions of cuboid.

Using Formula :

$\begin{gathered} {\underline{\boxed{ \rm {\blue{{\boxed{{ \red{ \rm{ \underbrace{Volume \: of \: Cuboid \: = \: Length × Breadth × Height}}}}}}}}}}}\end{gathered}$

Solution :

Let assume the dimensions of Cuboid be 5x , 4x and 3x.

• Where x is a multiple

Now , we have

• Length = 5x
• Breadth = 4x
• Height = 3x

Substuting the values in formula

${\textrm{{{\color{navy}{Volume \: of \: Cuboid \: = \: Length × Breadth × Height}}}}}$

$\begin{cases}{\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: 480 \: = \: (5x) \: \times \: (4x) \: \times \: (3x) \\ \\ {\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: 480 \: = 20x \: \times \: (3x) \\ \\ {\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: 480 \: = \: 60x \\ \\ {\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: \frac{48 \cancel0}{6 \cancel0} \: = \: x \\ \\ {\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: \cancel\frac{48}{6} \: = \: x \\ \\ {\large\bf{{\purple{ \longrightarrow}}}} \tt \: \: 8 \: = \: x \\ \\ {\large\bf{{\pink{ \implies}}}} \rm \: Value \: \: of \: \: x \: \: is \: \: 8 \end{cases}$

Now , putting the values of x in dimensions

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☯ Length of Cuboid = 5x

☯ Length of Cuboid = 5 × 8

☯ Length of Cuboid = 40

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☯ Breadth of Cuboid = 4x

☯ Breadth of Cuboid = 4 × 8

☯ Breadth of Cuboid = 32

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☯ Height of Cuboid = 3x

☯ Height of Cuboid = 3 × 8

☯ Height of Cuboid = 24

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⇛ Required dimensions are

• Length of Cuboid = 40 cm
• Breadth of Cuboid = 32 cm
• Height of Cuboid = 24 cm