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Question

A cylinder of maximum volume is cut from a wooden coboid of lenght 30 cm and a cross section a square of side 14 cm. Find the volume of the cylinder and vlome of wood wasted. 


Solution


In this answer  "π" is substitute as 22/7 which is 3.14
And multiplication represent as *

Given : Length of the cuboid = 30 cm
And having cross sections like squares of side 14 cm
So, height and breadth of cuboid is 14 cm.
For maximum possible volume of cylinder, 
Radius of cylinder = 7 cm
Length of the cuboid = height of the cylinder = 30 cm
So, 
Volume of cylinder = πr²h
= 22/7*7*7*30
Volume of the cylinder = 4620 cm³
Now,
Volume of the cuboid = L*B*H
= 30*14*14
Volume of the cuboid = 5880 cm³
Volume of the wood left as wasted = Volume of the cuboid - Volume of the cylinder
= 5880 - 4620
Volume of the wood wasted = 1260 cm³

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