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A cone of maximum volume is curved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the remaining wood.

Answer:

**Solution:**

Volume of the remaining wood can be calculated using the difference between the volume of cuboidal block of wood and volume of cone.

Given dimensions of the block of wood = 20 cm × 10 cm× 10 cm

Volume of the block of wood = 20×10×10 = 2000 cm^{3} [Volume = lbh]

Diameter of the cone, d = 10 cm

Radius of the cone , r = d/2 = 10/2 = 5 cm

Height of the cone, h = 20 cm

Volume of the cone = (1/3)π r^{2}h

= (1/3)×(22/7)×5^{2}×20

= (22×25×20)/(3×7)

= 11000/21 cm^{3}

Volume of the remaining wood = Volume of block of wood – Volume of cone

= 2000-11000/21

= (21×2000-11000)/21

= (42000-11000)/21

= 31000/21

= 1476.19 cm^{3}

**Hence the volume of the remaining wood is 1476.19 cm ^{3}.**

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