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Question
A cylindrical tube, open at both ends, is made of metal. The bore (internal diameter) of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal. Also, find the weight of the tube if 1 cm3 of the metal weighs 1.42 g.
Solution
Internal diameter of tube = 10.4cm
Internal radius = 5.2cm
Length of tube = 25cm
Thickness of metal = 8mm
Thickness of metal
= 8mm
= 0.8cm
Outer radius
= Internal radius + Thickness
= 5.2 + 0.8
= 6cm
Volume of metal
= Volume of material between outer radius and inner radius
= π(R2 - r2)h
= π(62 - (5.2)2} x 25
= 704cm3
∴ The volume of the metal used is 704cm3. ...(Ans 1)
1cm3 of metal = 1.42g
∴ 704cm3 of metal
= 704 x 1.42
= 999.68g
∴ The weight of the tube is 999.68g. ...(Ans 2)
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