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

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,

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

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

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

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

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

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

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

So,

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

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

Answer 2

$\rm{Since\:the\:length,\:breadth\: and\: height \:of \:a \:cuboid\:are\:in\:the\:ratio\:5:4:3}$

$\longrightarrow\textrm{Let the Length, Breadth and Height of Cuboid be 5a, 4a and 3a respectively}$

$\rm{Volume\:of\:Cuboid=Length\times Breadth\times Height}$

$\longrightarrow\rm{480\:cm^3=5a\times 4a\times 3a}\longrightarrow\rm{480\:cm^3=5\times 4\times 3\times a^3=60a^3}$

$\longrightarrow\rm{a^3=480\:cm^3/60=8\:cm^3}\longrightarrow\rm{a=\sqrt[\rm{3}]{\rm{8\:cm^3}}=\sqrt[\rm{3}]{\rm{8}}\:cm=2\:cm }$

$\bullet\textrm{ From the value of a, We can find Length, Breadth and Height of Cuboid!}$

$\longrightarrow\rm{Length\:of\: Cuboid=5a=5\times a= 5\times 2 \:cm=10\: cm}$

$\longrightarrow\rm{Breadth\:of\: Cuboid=4a=4\times a= 4\times 2 \:cm=8\: cm}$

$\longrightarrow\rm{Height\:of\: Cuboid=3a=3\times a= 3\times 2 \:cm=6\: cm}$