The diagonal of a cubical block of wood is 192 cm. Find its volume.

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 24 Jun, 2024 Shift 1)

Answer 1

Given:

Diagonal (d) = 192 cm

Formula used:

d = a√3

Where, a = side of the cube

Volume (V) = a³

Calculations:

192 = a√3

⇒ a = \(\frac{192}{\sqrt{3}}\)

⇒ Volume = \(\left(\frac{192}{\sqrt{3}}\right)^3\)

⇒ Volume = \(\frac{192\times 192\times 192}{(3\sqrt{3})}\)

⇒ Volume = \(64\times 192\times 64\sqrt3\)

⇒ Volume = \(786432\sqrt3\)

∴ The volume of the cubical block is \(786432\sqrt{3}\) cm³.