SSC MTS 2023 PYQ — Question 9

The correct answer is option 4 i.e. 307 : 216.

The volume of the cuboid is = l × b × h

⇒ 8 × 27 × 64 = 13824 cm³

The volume of the cube will be equal to the volume of the cuboid.

Hence¸

⇒ s³ = 13824

⇒ s = $^3\sqrt{13824}$

⇒ s = 24 cm

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

⇒ 2(l × b + b × h + h × l) : 6 × s²  

⇒ 2(8 × 27 + 27 × 64 + 64 × 8) : 6 × 24² = 2 × 2456  : 6 × 576

⇒ 4912 cm²  :  3456 cm²

⇒ 307 : 216