Question

If the length, breadth and height of a cuboid is in ratio of 5:4:3. If the volume of the cuboid is 480 cm'. Find it's length, breadth and height.​

Answer 1

Explanation:

volume of cuboid = l*b*h

volume of cuboid = l*b*h= 5x* 4x* 3x = 480

= 60x = 480

x = 480/60

x = 8

length = 5x = 5*8 = 40 cm

breadth = 4x = 4*8 = 32 cm

height = 3x = 3* 8 = 24 cm

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Answer 2

Given :

Ratio of length, breadth and height = 5:4:3

Volume of cuboid = 480 cm³

To find :

• Length
• Breadth
• Height

According to the question,

Let,

The ratio be :

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

Now,

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{Volume \: of \: cuboid = l \times b \times h}$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{408 = 5x \times 4x \times 3x}$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{480 = 60 \: {x}^{3} }$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{ \dfrac{480}{60} = {x}^{3} }$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{8 = {x}^{3} }$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{ \sqrt{8} = x }$

$\begin{gathered} \\ \end{gathered}$

$: \implies \sf{2 = x}$

$\begin{gathered} \\ \end{gathered}$

So,

• Length = 5x = 5 × 2 = 10 cm
• Breadth = 4x = 4 × 2 = 8 cm
• Height = 3x = 3 × 2 = 6 cm

$\begin{gathered} \\ \end{gathered}$

$\therefore { \underline{ \textsf { \textbf{So, the length, breadth and height is 10 cm, 8 cm and 6 cm. }}}}$