Question

A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?

Answer 1

The material left is 21 % of the volume (nearest to an integer) of the original cube if A right circular cylinder of maximum volume is cut out from a solid wooden cube

Step-by-step explanation:

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

Volume left  in % of original cube = 100 * (3/14)a³/ a³

= 150/7

= 21.4 %

Nearest integer = 21 %

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