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?

1 : 1

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