Question
What is the maximum number of pieces 1 cm in diameter
and 20 cm long that can be cut out of a cylindrical wooden block 20 cm in length and 3 cm in diameter?Solution
Radius (r) of given cylindrical wooden block = 3/2 cm (because Diameter = 2*radius) Length (h) = 20cm The volume of the block = ΟrΒ²h = Ο *(3/2)Β²* (20) = 45 Ο Now we need to find max number of pieces of 1 cm in diameter. So, radius = 1/2 cm, length = 20cm So, volume of the required block = Οr2h = Ο*(1/2)2*(20) = 5Ο So, max pieces = 45 Ο /5 Ο = 9 pieces.
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