A cylinder of Maximum volume is cut from a wooden cuboid of length 30 cm and cross section a square of side 14 cm .find volume of the cylinder and the volume of the wood wasted?
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Solution:-
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
Answer.
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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29
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