Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jul 7, 2025
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