Mathematics

A cylinder of maximum volume is cut out from a wooden cuboid of length 30 cm and cross section of square of side 14 cm. Find the volume of the cylinder and the volume of wood wasted.

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Largest size of cylinder cut out of the wooden cuboid will be of diameter = 14 cm, radius = $\dfrac{14}{2}$ = 7 cm and height = 30 cm.

Volume of cylinder = πr²h = $\dfrac{22}{7} \times 7 \times 7 \times 30$ = 22 × 7 × 30 = 4620 cm³.

Volume of cuboid = lbh = 30 × 14 × 14 = 5880 cm³.

Volume of wooden wasted = Volume of cuboid - Volume of cylinder = 5880 - 4620 = 1260 cm³.

Hence, the volume of cylinder = 4620 cm³ and volume of wooden wasted = 1260 cm³.

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