Question The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.
Video Explanation
Explanatory Answer
Volume of solid iron cuboid = volume of hollow cylindrical pipe
Volume of solid iron cuboid = 4.4 × 2.6 × 1 m3 .......... (1)
Volume of hollow cylindrical pipe = volume of outer cylinder – volume of inner cylinder
Radius of outer cylinder = 30 + 5 = 35 cm = \\frac{35}{100})m
Radius of inner cylinder = 30 cm = \\frac{30}{100})m
Volume of the outer cylinder = π × \(\frac {35} {100}{)}^{2}) × h, where h is the length of the pipe.
Volume of the inner cylinder = π × \(\frac {30} {100}{)}^{2}) × h
Volume of the pipe = \\frac{πh}{(100)^2}) (352 – 302)
= \\frac{22h}{7 × 10,000}) ((35 + 30)(35 – 30))
= \\frac{22h}{7 × 10,000})(65 × 5) m3 .......... (2)
Equating (1) and (2)
4.4 × 2.6 × 1 = \\frac{22h}{7 × 10,000}) (65 × 5)
Or h = \\frac{4.4 × 2.6 × 1 × 70,000}{22 ×65 ×5}) = 112m