A cuboid whose sides are 8 cm,9 cm and 24 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?

Correct option is A

Given:

Sides of the cuboid = 8 cm, 9 cm, 24 cm

Formula used:

The volume of the cuboid = Product of the sides

Solution:

Volume of cuboid = Product of the sides = 8 × 9 × 24 = 1728 cm³

Side of cube = cube root of the volume of cuboid = cube root of 1728 = 12 cm

Total surface area of cuboid = 2(lb + bh + hl) 

=> 2(8 × 9 + 9 × 24 + 24 × 8) 

=> 2(72 + 216 + 192) = 2(480) = 960 cm²

Total surface area of cube = 6(side)² = 6(12)² = 864 cm²

The respective ratio of the total surface area of the cuboid and cube

Ratio = 960 ∶ 864 = 10 ∶ 9

Hence, the correct option is (a).