Question

The volume of a cuboid is 7200 cm^3. Find the height of the cuboid if it's length, breadth and height are in the ratio 3:2:1
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Answer 1

$\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

${\sf{ ☞ \ Volume \ of \ cuboid \ = \ 7200cm³}}$

${\sf{☞ \ l:b:h \ = \ 3:2:1}}$

$\Large{\orange{\tt{\underline{\underline{To \ find \ :-}}}}}$

${\sf{↣ \ Height \ of \ cuboid}}$

$\Large{\green{\tt{\underline{\underline{Solution \ :-}}}}}$

Let the length, breadth and height be 3x, 2x and x.

As we know that,

${\sf{↣ \ Volume \ of \ cuboid \ = \ l×b×h}}$

${\sf{↣ \ 7200 \: = \: 3x \times 2x \times x}}$

${\sf{ ↣ \ 7200 \: = \: 6 {x}^{3} }}$

${\sf{ ↣ \ {x}^{3} \: = \frac{7200}{6}}}$

${\sf{ ↣ \ x \: = \: \sqrt[3]{1200}}}$

${\sf{↣ \ x \: = 10.62 \: cm}}$

Now,

${\sf{↣ \ Height \: = \: x}}$

${\sf{↣ \ Height \: = \: 10.62 \: cm}}$

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