Question

The dimensions of a cuboid are in the ratio 3:2:1 and the total surface area is 1408 sq.cm. Find its volume.​

Answer 1

Answer:

Let the length of the cuboid =x, breadth =2x, height =3x

Total surface area of a cuboid =2(l×b+b×h+l×h)

Given, total surface area of the cuboid =88m

2⇒2(x×2x+2x×3x+x×3x)=88m

2 ⇒22x 2=88⇒x=2

Hence, the length of the cuboid =x=2m, breadth =2x=4m, height =3x=6m

I hope it will help you...

Answer 2

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

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

${\sf{❥ \ Ratio \ of \ sides \ of \ cuboid \ = \ 3:2:1}}$

${\sf{❥ \ Total \ surface \ area \ = \ 1408 cm²}}$

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

${\sf{• \ Volume \ of \ cuboid }}$

$\Large{\purple{\tt{\underline{\underline{Formula \ used \ :-}}}}}$

${\sf{Total \ surface \ area \ of \ cuboid \ = \ 2(lb+bh+lh)}}$

and

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

here,

• l is length
• b is breadth, and
• h is height

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

${\tt{Let \ length \ breadth \ and }} \\{\tt{ height \ be \ 3x, \ 2x \ and \ x \ cm \ respectively. }}$

${\bf{\large{✯ \ Total \ surface \ area \ = \ 2(lb+bh+lh)}}}$

${\sf{ \leadsto \ 1408 \ = \ 2(3x×2x \ + \ 2x×x \ + \ 3x×x)}}$

${\sf{\leadsto \ 1408 \ = \ 2(6x²+2x²+3x²)}}$

${\sf{\leadsto \ 1408 \ = \ 2×11x²}}$

${\sf{\leadsto \ 1408 \ = \ 22x²}}$

${\sf{\leadsto \ x² \ = \ \frac{\cancel{1408}}{\cancel{22}}}}$

${\sf{\leadsto \ x \ = \ \sqrt{64}}}$

${\sf{\leadsto \ x \ = \ 8cm}}$

• length = 3x ⟹ 24cm
• breadth = 2x ⟹ 16cm
• height = x ⟹ 8cm

_______________________________________

${\bf{\large{✯ \ Volume \ = \ l×b×h}}}$

${\sf{\longmapsto \ Volume \ = \ 24×16×8}}$

${\sf{\longmapsto \ Volume \ = \ 307cm³}}$

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$\Large\mathcal{\fcolorbox{lime}{black}{\red{Hope it's help ⚓⚓}}}$

$\large\mathcal{\fcolorbox{yellow}{teal}{\orange{Please mark me as brainliest (. ❛ ᴗ ❛.)}}}$