Question

The length,breadth and height of a cuboid are in the ratio 3:2:1.It's volume is 384 cm^3.Find the total surface area of the cuboid.


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Answer 1

HEY MATE HERE IS YOUR ANSWER

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Given :-

Volume of cuboid = 384 cm^3

Ratio :- 3 : 2 : 1

Let be x

ATQ

3x + 2x + 1x = 384

6x = 384

➡️ x = 384/6

➡️ x = 64

Length :- 3x = 3(64) = 192 cm

Breadth :- 2x = 2(64) = 128 cm

Height :- x = 64 cm


Surface area of cuboid :- 2(L + B) h

2 ( 192 + 128) 64

2(320) 64

640 × 64

➡️ 40960 cm^2






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Answer 2

$<b>Heya mate. (^_-). Solution below.$
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♦ Let the common ratio between length, breadth and height be x.


Then,

length (l) = 3x

breadth (b) = 2x

height (h) = x



♦ Then, volume
= l × b × h
= 3x × 2x × x
= 6x³



♦ But, given volume = 384 cm³

=> 6x³ = 384

=> x³ = 384/6

=> x³ = 64

=> x = ³√64

=> x = ³√4 × 4 × 4

=> x = 4



•°• Length = 3x = 3(4) = 12 cm

Breadth = 2x = 2(4) = 8 cm

Height = x = 4 cm



♦ Now, Total surface area (T.S.A) of a cuboid,

= 2(lb + bh + hl)

= 2 [(12 × 8) + (8 × 4) + (4 × 12)]

= 2 (96 + 32 + 48)

= 2 (176)

= 352 cm².



♥ Hence, total surface area of the cuboid is 352 cm²
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Thank you.. ^_^