Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm.
Use \(\pi\) = \(\frac{22}{7}\)

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 1)

Answer 1

Given:

Edge of the cube = 8 cm

Formula Used:

For the largest right circular cone cut from a cube:

Diameter of the base of the cone = Edge of the cube

Height of the cone = Edge of the cube

Volume of a cone = 1/3 × π × r² × h

Where, r = radius, h = height

Calculations:

Diameter of the cone = 8 cm

⇒ Radius (r) = 8/2 = 4 cm

Height (h) = 8 cm

Volume of the cone = 1/3 × (22/7) × 4² × 8

⇒ Volume of the cone = 1/3 × (22/7) × 16 × 8

⇒ Volume of the cone = (22 × 16 × 8) / (3 × 7)

⇒ Volume of the cone = 2816 / 21

⇒ Volume of the cone ≈ 134\(\frac{2}{21}\) cm³

∴ The volume of the largest right circular cone that can be cut out from a cube with an edge of 8 cm is 134\(\frac{2}{21}\) cm3