The curved surface area of a right circular cylindrical wooden log of uniform density is 440 sq. decimeters. The weight of 1 cubic decimeter of wood is 3 kg and the weight of a log is 18.48 quintals. Find the diameter of the log.
Given:
- Curved surface area = 440 sq. decimeters
- Density of the wood = 3 kg per cubic decimeter
- Weight of the log = 18.48 quintals (1 quintal = 100 kg)
Convert the weight of the log to kilograms:
Weight of the log = 18.48 × 100 = 1848 kg
Formula for the curved surface area (CSA) of a cylinder:
CSA = 2πrh
Given that CSA = 440:
2πrh = 440 — (1)
Volume of the cylinder:
Volume = πr²h
Weight of the log = Volume × Density
1848 = πr²h × 3
πr²h = 616 — (2)
Divide the second equation by the first:
πr²h \over 2πrh = 616 \over 440
r \over 2 = 14 \over 10
r = 2.8 decimeters
Diameter = 2r = 2 × 2.8 = 5.6 decimeters
Therefore, the diameter of the log is 5.6 decimeters.
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