SSC CGL 2026 PYQ — Question 4

The correct answer is Option 3 i.e.  6 cm³.

Let edges be a cm, b cm, and c cm

$\sqrt{a^2 + b^2} = \sqrt{5}$ ⇒ $a^2 + b^2 = 5$ ...(1)

$\sqrt{b^2 + c^2} = \sqrt{10}$ ⇒ $b^2 + c^2 = 10$ ...(2)

$\sqrt{a^2 + c^2} = \sqrt{13}$ ⇒ $a^2 + c^2 = 13$ ...(3)

Add (1) and (2): a² + 2b² + c² = 5 + 10 = 15

⇒ 13 + 2b² = 15

⇒ 2b² = 15 - 13 = 2

⇒ b² = 1

⇒ b = 1

a² + b² = 5 ⇒ a² + 1 = 5 ⇒ a² = 4 ⇒ a = 2

a² + c² = 13 ⇒ 4 + c² = 13 ⇒ c² = 9 ⇒ c = 3

Volume = a × b × c = 2 × 1 × 3 = 6 cm³