The radius of a sphere and that of the base of a cylinder are equal. The ratio of the radius of the base of the cylinder and the height of the cylinder is 3 : 4. What is the ratio of the volume of the sphere to that of the cylinder?
Answer & explanation
Correct answer: option 3
We know that,
Volume of Sphere = \(\frac{4}{3}\)πr3
Volume of Cylinder = πr2h
We have,
Radius of the sphere = radius of the cylinder
Ratio of radius to height of cylinder = 3 : 4
Let the height of the cylinder = 4a
Then, radius of the cylinder, r = 3a
So, Volume of Sphere = \(\frac{4}{3}\) × π × (3x)3 = 36πx3
And, Volume of Cylinder = π × (3x)2 × 4x = 36πx3
Ratio of the volume of sphere to that of the cylinder = 36πx3 : 36πx3 = 1:1