A cylinder of maximum possible size is cut from a solid wooden cube. The remaining material of the cube is what percentage of the original cube?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 21.5
A right circular cylinder of maximum volume is cut out from a solid wooden cube
Let say cube side = a
Volume of Cube = a³
A right circular cylinder of maximum volume
⇒ Height = a
Diameter = a
Radius = a/2
Right circular cylinder of maximum volume = π (a/2)² × a
= (π/4)a³ [Using π = 22/7]
= (11/14) a³
Volume left = a³ - (11/14) a³ = (3/14)a³
Hence,
Volume left in % of original cube = 100 × (3/14)a³/ a³
= 150/7 = 21.5%