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A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me....
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A sphere and cube have a same surface area.so,Prove that ratio of volu...
Let r and a be the radius of the sphere and edge of the cube respectively.Given, Surface area of sphere = Surface area of cube4πr2 = 6a2(r/a)2 = 3 / 2πr / a = √(3/2π)Volume of sphere / Volume of cube = (4/3)πr3 / a3 = (4π/3)(r/a)3= (4π/3)(√(3/2π))3= (4π/3)(3/2π)(√(3/2π))= 2√(3/2π)= √(4x3/2π)= √(6/π)Thus, Volume of sphere : Volume of cube = √6 : √π.
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A sphere and cube have a same surface area.so,Prove that ratio of volu...
Proof of Ratio of Volume of Cube to Volume of Sphere
- Given: Surface area of sphere = Surface area of cube
- Let:
- Side of cube = x
- Radius of sphere = r
- Surface Area of Cube:
- 6x^2 = 4πr^2
- x = √(2/3) r
- Volume of Cube:
- V_cube = x^3 = (2/3)√(2/3) r^3
- Surface Area of Sphere:
- 4πr^2 = 6x^2
- r = √(3/8) x
- Volume of Sphere:
- V_sphere = (4/3)πr^3 = (1/2)√(3/2)π x^3
- Ratio of Volume:
- V_cube : V_sphere = (2/3)√(2/3) r^3 : (1/2)√(3/2)π x^3
- V_cube : V_sphere = √6 : √π
This proves that the ratio of the volume of the cube to the volume of the sphere is √6 : √π.
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A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me....
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A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.... 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 A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.... covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.....
A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.... 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 A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.... covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sphere and cube have a same surface area.so,Prove that ratio of volume of cube to that of volume of sphere is √6:√π.....?????plz reply me.....
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