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The radius of a cylinder is the same as that of a sphere. There volumes are equal. The height of the cylinder is how many times of its radius?
  • a)
    1
  • b)
    2
  • c)
    2/3
  • d)
    4/3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The radius of a cylinder is the same as that of a sphere. There volum...
Radius of cylinder = Radius of sphere and volume of cylinder = volume of sphere
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The radius of a cylinder is the same as that of a sphere. There volum...
Problem:
The radius of a cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is how many times its radius?

Solution:
Let's assume the radius of the cylinder and sphere to be 'r'. We need to find the height of the cylinder in terms of 'r'.

Volume of a Cylinder:
The volume of a cylinder is given by the formula:
Vcylinder = π * r^2 * h

Volume of a Sphere:
The volume of a sphere is given by the formula:
Vsphere = (4/3) * π * r^3

Given:
Vcylinder = Vsphere

Substituting the formulas:
π * r^2 * h = (4/3) * π * r^3

Cancelling out π and r^2:
h = (4/3) * r

Therefore, the height of the cylinder is (4/3) times its radius.

Answer:
The height of the cylinder is (4/3) times its radius. Hence, the correct answer is option 'D'.
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The radius of a cylinder is the same as that of a sphere. There volumes are equal. The height of the cylinder is how many times of its radius?a)1b)2c)2/3d)4/3Correct answer is option 'D'. Can you explain this answer?
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