A cuboid of sides 12 cm, 18 cm and 27 cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to that of the cube?

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SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 4)
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  1. 18 : 17
  2. 17 : 19
  3. 19 : 18
  4. 19 : 17

Answer (Detailed Solution Below)

Option 3 : 19 : 18
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Detailed Solution

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Given:

Sides of cuboid are 12cm, 18cm and 27cm.

Formula used:

Volume of cuboid = l × b × h

Volume of cube = a3

Surface area of the cuboid = 2(l x b + b x h + l x h)

Surface area of the cube = 6 a2

Where a’ is side of cube, and l,b,h are sides of cuboid.

Calculation

Volume of cuboid = 12 × 18 × 27 = 5832 cm3

Volume of cube = a3 = 5832 

=> a = 18 cm

Surface area of the cuboid  = 2( 12 x 18 + 18 x 27 + 12 x 27)

=> 2(216 + 486 + 324)

=> 2 x 1026 = 2052

Surface area of the cube = 6 x 18 x 18 = 1944

Now,

The ratio of the total surface area of the cuboid to that of the cube

=>  2052 : 1944

=> 19 x 108 : 18 x 108

=> 19 : 18

Hence '19: 18' is the correct answer.

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