A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
Answers
Answer:
The length of a pipe is 2698.18 cm
Step-by-step explanation:
Given :
Let the length of a pipe be ‘h’ .
Dimension of a solid cuboid of iron = 53 cm ⨯ 40 cm ⨯ 15 cm
Outer diameter of a pipe = 8 m
Outer radius of a cylindrical pipe, R = 8/2 = 4 cm
Inner diameter of a cylindrical pipe = 7
Inner radius of a cylindrical pipe , r = 7/2 = 3.5 cm
Since, the solid cuboid of iron is melted and recast into a cylindrical pipe , so volume of both are equal
Volume of cuboid = Volume of hollow cylindrical pipe
l × b × h = π(R² - r²)h
53 x 40 x 15 = 22/7 × h (4² - 3.5²)
53 x 40 x 15 = 22/7 × h (16 - 12.25)
53 x 40 x 15 = 22/7 × h × 3.75
h = (53 x 40 x 15 × 7) / 22 × 3.75
h = 222600 / 82.5
h = 2698.18 cm
Hence, the length of a pipe is 2698.18 cm.
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Let the length of a pipe be ‘h’ .
Dimension of a solid cuboid of iron = 53 cm ⨯ 40 cm ⨯ 15 cm
Outer diameter of a pipe = 8 m
Outer radius of a cylindrical pipe, R = 8/2 = 4 cm
Inner diameter of a cylindrical pipe = 7
Inner radius of a cylindrical pipe , r = 7/2 = 3.5 cm
Since, the solid cuboid of iron is melted and recast into a cylindrical pipe , so volume of both are equal
Volume of cuboid = Volume of hollow cylindrical pipe
l × b × h = π(R² - r²)h
53 x 40 x 15 = 22/7 × h (4² - 3.5²)
53 x 40 x 15 = 22/7 × h (16 - 12.25)
53 x 40 x 15 = 22/7 × h × 3.75
h = (53 x 40 x 15 × 7) / 22 × 3.75
h = 222600 / 82.5
h = 2698.18 cm
Hence, the length of a pipe is 2698.18 cm