#### 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 m^{3} .......... (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}) (35^{2} – 30^{2})

= \\frac{22h}{7 × 10,000}) ((35 + 30)(35 – 30))

= \\frac{22h}{7 × 10,000})(65 × 5) m^{3} .......... (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