Question

a cylinder of maximum volume is cut from a wooden cuboid of lenghth 30cm. and cross section of a square of side 14 cm . find the volume of the wood wasted.

Answer 1

Hi,

i)Dimensions of the wooden cuboid ;

Length = l = 30 cm

Breadth = b = 14 cm

Heightb = h = 14 cm

Volume of the cuboid = lbh

V 1= 30 cm × 14 cm × 14 cm

V1 = 5880 cm^3 ------ ( 1 )

ii )dimensions of maximum cylinder cut from the wooden cuboid are,

Radius( r ) =square side /2

= 14/2 = 7 cm

Height = H= cuboid height

H = 30 cm

Volume of the cylinder = pi× r^2 × H

V2 = ( 22/ 7 ) × 7 ^2 × 30

V2 = 4620 cm^3---------( 2 )

Volume of wood wasted

= V1 - V2

= 5880 cm^3 - 4620 cm^3

= 1260 cm^3

I hope this helps you.

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