Question

The edges of a cuboid are in the ratio 1:2:3 and is surface area is 88 cm². The volume of the cu
(i) 48 cm³
(ii) 64 cm³
(iii) 96 cm ³
(iv) 120 can ³
​

Answer 1

Answer:

$\Large{\underline{\underline{\bf{To FiNd:-}}}}$

Volume of the Cuboid .

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

Ratio of edges of cuboid = 1 : 2 : 3

Surface area = 88cm²

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let,

( Length ) ↠ x

( Breadth ) ↠ 2x

( Height ) ↠ 3x

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Surface area = 88cm²

❥ 2( lb + bh + hl ) = 88cm²

❥ 2{ χ × 2χ + 2χ × 3χ + 3χ × χ } = 88cm²

❥ 2 ( 2χ² + 6χ² + 3χ² ) = 88

❥ 2 × 11χ² = 88

❥ 11χ² = 88/2

❥ 11χ² = 44

❥ χ² = 44/ 11

❥ χ² = 4

❥ χ = √4

↠[ χ ➩ 2 ]

Now,

The Value of χ ➼ 2

Then,

Length = χ ➼ 2cm

Breadth = 2χ ➼ 2 × 2 = 4cm

Height = 3χ ➼ 3 × 2 = 6cm

Therefore ,

Volume of Cuboid ➩ ( L × B × H )

❥ 2 × 4 × 6

❥ 48cm³

Hence ,

The option ( A ) is correct .

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Required Formulas ➤

❧ Surfαcє αrєα σf cuвσíd ➼ 2 (lєngth х вrєαdth + вrєαdth х hєíght + lєngth х hєíght)

❧ Vσlumє σf thє cuвσíd ➼ (lєngth × вrєαdth × hєíght)

Other Important Formulas :--

❧ Díαgσnαl σf thє cuвσíd ➼ √( l² + в² +h²)

❧ Pєrímєtєr σf cuвσíd ➼ 4 (lєngth + вrєαdth + hєíght)

❧ Lαtєrαl surfαcє αrєα ➼ 2 hєíght(lєngth + вrєαdth)

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