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The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder
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Volume of the Hollow Sphere
To find the diameter and curved surface area of the cylinder formed from the hollow sphere, we first need to calculate the volume of the hollow sphere.
- Formula for Volume of Hollow Sphere
Volume = (4/3)π(R^3 - r^3)
Where R is the external radius and r is the internal radius.
- Values
External radius (R) = 5 cm
Internal radius (r) = 3 cm
- Calculation of Volume
Volume = (4/3)π(5^3 - 3^3)
= (4/3)π(125 - 27)
= (4/3)π(98)
= 392π cm³
Volume of the Cylinder
The hollow sphere is melted to form a solid cylinder with a height of 22/3 cm.
- Formula for Volume of Cylinder
Volume = πr²h
Where r is the radius and h is the height.
- Substituting the Known Height
Volume = πr²(22/3)
- Equating the Volumes
392π = πr²(22/3)
Cancelling π:
392 = r²(22/3)
- Solving for r²
r² = 392 * (3/22)
r² = 53.4545
r ≈ 7.31 cm
Diameter of the Cylinder
- Calculating Diameter
Diameter = 2r ≈ 2 * 7.31 ≈ 14.62 cm
Curved Surface Area of the Cylinder
- Formula for Curved Surface Area
Curved Surface Area = 2πrh
- Substituting Values
Curved Surface Area = 2π(7.31)(22/3)
= 2π(7.31)(7.33)
≈ 1064.82 cm²
Summary
- Diameter of the Cylinder: ≈ 14.62 cm
- Curved Surface Area of the Cylinder: ≈ 1064.82 cm²
To find the diameter and curved surface area of the cylinder formed from the hollow sphere, we first need to calculate the volume of the hollow sphere.
- Formula for Volume of Hollow Sphere
Volume = (4/3)π(R^3 - r^3)
Where R is the external radius and r is the internal radius.
- Values
External radius (R) = 5 cm
Internal radius (r) = 3 cm
- Calculation of Volume
Volume = (4/3)π(5^3 - 3^3)
= (4/3)π(125 - 27)
= (4/3)π(98)
= 392π cm³
Volume of the Cylinder
The hollow sphere is melted to form a solid cylinder with a height of 22/3 cm.
- Formula for Volume of Cylinder
Volume = πr²h
Where r is the radius and h is the height.
- Substituting the Known Height
Volume = πr²(22/3)
- Equating the Volumes
392π = πr²(22/3)
Cancelling π:
392 = r²(22/3)
- Solving for r²
r² = 392 * (3/22)
r² = 53.4545
r ≈ 7.31 cm
Diameter of the Cylinder
- Calculating Diameter
Diameter = 2r ≈ 2 * 7.31 ≈ 14.62 cm
Curved Surface Area of the Cylinder
- Formula for Curved Surface Area
Curved Surface Area = 2πrh
- Substituting Values
Curved Surface Area = 2π(7.31)(22/3)
= 2π(7.31)(7.33)
≈ 1064.82 cm²
Summary
- Diameter of the Cylinder: ≈ 14.62 cm
- Curved Surface Area of the Cylinder: ≈ 1064.82 cm²
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The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder
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The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder.
The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The internal and external radius of a hollow sphere are 3 and 5 respectively the sphere is melted to form a solid cylinder of height 22 by 3 cm find the diameter and curved surface area of cylinder.
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