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A sphere and cube have same surface. What is ratio of volume of sphere to cube?
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A sphere and cube have same surface. What is ratio of volume of sphere...
Let r and a be the radius of the sphere and edge of the cube respectively.
Given, Surface area of sphere = Surface area of cube
4πr2 = 6a2
(r/a)2 = 3 / 2π
r / 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.
Given, Surface area of sphere = Surface area of cube
4πr2 = 6a2
(r/a)2 = 3 / 2π
r / 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 same surface. What is ratio of volume of sphere to cube?
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A sphere and cube have same surface. What is ratio of volume of sphere to cube? 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 same surface. What is ratio of volume of sphere to cube? 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 same surface. What is ratio of volume of sphere to cube?.
A sphere and cube have same surface. What is ratio of volume of sphere to cube? 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 same surface. What is ratio of volume of sphere to cube? 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 same surface. What is ratio of volume of sphere to cube?.
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