The dimensions of a solid iron cuboid are 4.4 m x 2.6 m x 1 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.
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Length , l = 4.4 metres
Breadth , b = 2.6 metres
Height , h = 1 metre
Volume of a cuboid = l b h
= 4.4 × 2.6 × 1
= 11.44 m³
The cuboid is melted and is made into a hollow cylindrical pipe.
But ,
Even if shape changes ,Volume of both the shapes remains same.
Volume of cuboid = Volume of hollow cylindrical pipe = 11.44 m³
Radius ,r = 30 cm = 0.3 metres
Thickness = 5 cm = 0.05 metre
Outer radius, R = inner radius + thickness
= 0.3 + 0.05
= 0.35 metres
Height of the pipe = Length of the pipe
Volume of a cylindrical pipe = π [ R² - r ² ] × h
= \frac{22}{7}
7
22
× [ (0.35)² - (0.3)² ] ×h
\frac{22}{7}
7
22
× [ (0.35)² - (0.3)² ] ×h = 11.44 m³
\frac{22}{7}
7
22
× [ 0.1225 - 0.09 ] ×h = 11.44 m³
\frac{22}{7}
7
22
× 0.0325 × h = 11.44 m³
h = \frac{11.44 * 7}{22 *0.0325 }
22∗0.0325
11.44∗7
= \frac{80.08}{0.715 }
0.715
80.08
= 112 metres
Length of the pipe = 112 metres