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A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.?
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A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is...
**Given Information:**
- Base area of the cuboidal brass piece = 11 dm^2
- Height of the cuboidal brass piece = 0.2 dm
- Diameter of the cylindrical wire = 0.25 cm
**To Find:**
The length of the wire formed by drawing the cuboidal brass piece.
**Solution:**
To find the length of the wire, we need to find the volume of the cuboidal brass piece and then use it to calculate the length of the cylindrical wire.
1. **Finding the Volume of the Cuboidal Brass Piece:**
- The volume of a cuboid is given by the formula: V = l * b * h, where l is the length, b is the breadth, and h is the height.
- In this case, the base area (11 dm^2) is equal to the product of length (l) and breadth (b): l * b = 11 dm^2.
- The height (h) of the cuboidal piece is given as 0.2 dm.
- Substituting the values, we get: l * b * 0.2 = 11 dm^2.
- Simplifying the equation, we get: l * b = 55 dm^2.
2. **Finding the Length and Breadth of the Cuboidal Brass Piece:**
- To find the length and breadth, we can assume any two positive integers that multiply to give 55 (the product of length and breadth).
- The possible combinations are: (1, 55), (5, 11), and (11, 5).
- Since the base area is given as 11 dm^2, the length and breadth cannot be 1 and 55, as it would result in a base area of 55 dm^2.
- Therefore, the length and breadth of the cuboidal brass piece are 5 dm and 11 dm, respectively.
3. **Finding the Volume of the Cuboidal Brass Piece:**
- The volume of the cuboidal brass piece can now be calculated using the formula: V = l * b * h.
- Substituting the values, we get: V = 5 dm * 11 dm * 0.2 dm = 11 dm^3.
4. **Finding the Length of the Cylindrical Wire:**
- The volume of the cylindrical wire is equal to the volume of the cuboidal brass piece.
- The volume of a cylinder is given by the formula: V = π * r^2 * h, where r is the radius and h is the height.
- The diameter of the cylindrical wire is given as 0.25 cm, which means the radius is half of the diameter: r = 0.25 cm / 2 = 0.125 cm.
- Converting the radius to dm: 0.125 cm = 0.0125 dm.
- Substituting the values, we get: 11 dm^3 = π * (0.0125 dm)^2 * h.
- Solving the equation for h, we get: h = 11 dm^3 / (π * (0.0125 dm)^2).
- Calculating the value of h using the appropriate value of π (3.14), we get: h ≈
- Base area of the cuboidal brass piece = 11 dm^2
- Height of the cuboidal brass piece = 0.2 dm
- Diameter of the cylindrical wire = 0.25 cm
**To Find:**
The length of the wire formed by drawing the cuboidal brass piece.
**Solution:**
To find the length of the wire, we need to find the volume of the cuboidal brass piece and then use it to calculate the length of the cylindrical wire.
1. **Finding the Volume of the Cuboidal Brass Piece:**
- The volume of a cuboid is given by the formula: V = l * b * h, where l is the length, b is the breadth, and h is the height.
- In this case, the base area (11 dm^2) is equal to the product of length (l) and breadth (b): l * b = 11 dm^2.
- The height (h) of the cuboidal piece is given as 0.2 dm.
- Substituting the values, we get: l * b * 0.2 = 11 dm^2.
- Simplifying the equation, we get: l * b = 55 dm^2.
2. **Finding the Length and Breadth of the Cuboidal Brass Piece:**
- To find the length and breadth, we can assume any two positive integers that multiply to give 55 (the product of length and breadth).
- The possible combinations are: (1, 55), (5, 11), and (11, 5).
- Since the base area is given as 11 dm^2, the length and breadth cannot be 1 and 55, as it would result in a base area of 55 dm^2.
- Therefore, the length and breadth of the cuboidal brass piece are 5 dm and 11 dm, respectively.
3. **Finding the Volume of the Cuboidal Brass Piece:**
- The volume of the cuboidal brass piece can now be calculated using the formula: V = l * b * h.
- Substituting the values, we get: V = 5 dm * 11 dm * 0.2 dm = 11 dm^3.
4. **Finding the Length of the Cylindrical Wire:**
- The volume of the cylindrical wire is equal to the volume of the cuboidal brass piece.
- The volume of a cylinder is given by the formula: V = π * r^2 * h, where r is the radius and h is the height.
- The diameter of the cylindrical wire is given as 0.25 cm, which means the radius is half of the diameter: r = 0.25 cm / 2 = 0.125 cm.
- Converting the radius to dm: 0.125 cm = 0.0125 dm.
- Substituting the values, we get: 11 dm^3 = π * (0.0125 dm)^2 * h.
- Solving the equation for h, we get: h = 11 dm^3 / (π * (0.0125 dm)^2).
- Calculating the value of h using the appropriate value of π (3.14), we get: h ≈
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A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is...
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A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.?
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A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.?.
A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cuboidal piece of brass having a base of 11dm^2 and height 0.2 dm is drawn into a cylindrical wire of 0.25cm in diameter. Find the length of the wire.?.
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