Question

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

Answer 1

Length of the cuboid = 30 cm

And having cross sections like squares of side 14 cm

Height and breadth of cuboid = 14 cm.

For maximum possible volume of cylinder, 

Radius of cylinder = 7 cm

Length of the cuboid = height of the cylinder = 30 cm

Volume of cylinder = πr²h

= $\frac{22}{7}$ × $\frac{7}{1}$ ×$\frac{7}{1}$ × $\frac{30}{1}$

Volume of the cylinder = 4620 cm³

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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