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A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe?
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Given:
- Dimensions of the solid cuboid: 53cm × 40cm × 15cm
- Outer diameter of the cylindrical pipe: 8cm
- Inner diameter of the cylindrical pipe: 7cm
To find: The length of the pipe
Solution:
To find the length of the pipe, we need to first calculate the volume of the solid cuboid and then equate it to the volume of the cylindrical pipe.
Step 1: Calculate the volume of the solid cuboid
The volume of a cuboid is given by the formula:
Volume = length × width × height
Given dimensions of the solid cuboid:
Length = 53cm
Width = 40cm
Height = 15cm
Using the formula, we can calculate the volume:
Volume = 53cm × 40cm × 15cm
Volume = 31800 cm³
Step 2: Calculate the volume of the cylindrical pipe
The volume of a cylinder is given by the formula:
Volume = π × r² × h
Given dimensions of the cylindrical pipe:
Outer diameter = 8cm
Radius of outer diameter = 8cm / 2 = 4cm
Inner diameter = 7cm
Radius of inner diameter = 7cm / 2 = 3.5cm
Using the formula, we can calculate the volume:
Volume = π × (4cm)² × h - π × (3.5cm)² × h
Volume = π × 16cm² × h - π × 12.25cm² × h
Volume = π × (16cm² - 12.25cm²) × h
Volume = π × 3.75cm² × h
Step 3: Equate the volumes and solve for the length of the pipe
Since the volume of the solid cuboid is equal to the volume of the cylindrical pipe, we can equate the two volumes:
31800 cm³ = π × 3.75cm² × h
To solve for h (length of the pipe), divide both sides of the equation by π × 3.75cm²:
h = 31800 cm³ / (π × 3.75cm²)
h ≈ 276.6 cm
Therefore, the length of the pipe is approximately 276.6 cm.
- Dimensions of the solid cuboid: 53cm × 40cm × 15cm
- Outer diameter of the cylindrical pipe: 8cm
- Inner diameter of the cylindrical pipe: 7cm
To find: The length of the pipe
Solution:
To find the length of the pipe, we need to first calculate the volume of the solid cuboid and then equate it to the volume of the cylindrical pipe.
Step 1: Calculate the volume of the solid cuboid
The volume of a cuboid is given by the formula:
Volume = length × width × height
Given dimensions of the solid cuboid:
Length = 53cm
Width = 40cm
Height = 15cm
Using the formula, we can calculate the volume:
Volume = 53cm × 40cm × 15cm
Volume = 31800 cm³
Step 2: Calculate the volume of the cylindrical pipe
The volume of a cylinder is given by the formula:
Volume = π × r² × h
Given dimensions of the cylindrical pipe:
Outer diameter = 8cm
Radius of outer diameter = 8cm / 2 = 4cm
Inner diameter = 7cm
Radius of inner diameter = 7cm / 2 = 3.5cm
Using the formula, we can calculate the volume:
Volume = π × (4cm)² × h - π × (3.5cm)² × h
Volume = π × 16cm² × h - π × 12.25cm² × h
Volume = π × (16cm² - 12.25cm²) × h
Volume = π × 3.75cm² × h
Step 3: Equate the volumes and solve for the length of the pipe
Since the volume of the solid cuboid is equal to the volume of the cylindrical pipe, we can equate the two volumes:
31800 cm³ = π × 3.75cm² × h
To solve for h (length of the pipe), divide both sides of the equation by π × 3.75cm²:
h = 31800 cm³ / (π × 3.75cm²)
h ≈ 276.6 cm
Therefore, the length of the pipe is approximately 276.6 cm.
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Question Description
A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe?.
A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cuboid of iron with dimensions 53cm × 40cm ×15cm is melted into a cylindrical pipe the outer and inner dimensions of pipe are 8cm and 7cm respectively. Find the length of pipe?.
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