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If the volume and the surface area of a sphere are numerically equal, then the numerical value of the radius of the sphere is.
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the volume and the surface area of a sphere are numerically equal,...
Volume of sphere = Surface area of sphere
4/3πr3 = 4πr2 [where r - radius]
⇒ r = 3
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If the volume and the surface area of a sphere are numerically equal,...
Approach:
To solve this problem, we need to use the formulas for the volume and surface area of a sphere and set them equal to each other. Then we can solve for the radius of the sphere.
Given:
Volume of sphere = Surface area of sphere
Formulas:
Volume of sphere = (4/3)πr^3
Surface area of sphere = 4πr^2
Equation:
(4/3)πr^3 = 4πr^2
Solving for r:
Divide both sides by 4π:
(4/3)r = r^2
4r = 3r^2
r = 3
Therefore, the numerical value of the radius of the sphere is 3. Hence, the correct answer is option 'c) 3'.
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If the volume and the surface area of a sphere are numerically equal, then the numerical value of the radius of the sphere is.a)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?
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