a cylinder of maximum volume is cut from a wooden cuboid of length 30cm and cross section a square of side 14cm . find the volume of the cylinder and the volume of the wood wasted
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Heya
Here goes your answer
Volume of cuboid = lbh
l=30cm b=14cm h =14cm
Volume of cuboid = 30 × 14 × 14
= 30 × 196
= 5880cm^3
A cylinder of max volume was carved out of the cuboid
So the radius of the base of the cylinder will be half the side of the square base of cuboid.
The height of cylinder will be the length of the cuboid
=> Radius = 14/2 = 7cm
Height = 30 cm
Volume of cylinder = πr^2h
= 22/7 × 7 × 7 × 30
= 4620cm^3
Volume of wood wasted = volume of cuboid - volume of cylinder
= 5880- 4620
= 1260cm^3
Hope it helps
Here goes your answer
Volume of cuboid = lbh
l=30cm b=14cm h =14cm
Volume of cuboid = 30 × 14 × 14
= 30 × 196
= 5880cm^3
A cylinder of max volume was carved out of the cuboid
So the radius of the base of the cylinder will be half the side of the square base of cuboid.
The height of cylinder will be the length of the cuboid
=> Radius = 14/2 = 7cm
Height = 30 cm
Volume of cylinder = πr^2h
= 22/7 × 7 × 7 × 30
= 4620cm^3
Volume of wood wasted = volume of cuboid - volume of cylinder
= 5880- 4620
= 1260cm^3
Hope it helps
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