The volume of sphere is given by V = 4/3 πR³ where R is the radius of sphere. Find the rate of change of volume with respect to R.

Solution:

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

We know the volume of sphere,

V = 4/3 πR³

To find the rate of change of volume with respect to R.

Differentiate the volume with respect to R.

⇒ dV/dR = 4/3 π d/dR (R³)

⇒ dV/dR = 4/3 × π × 3R²

On simplification,

⇒ dV/dR = 4πR²

Therefore, the rate of change of volume with respect to R is 4πR².

The volume of sphere is given by V = 4/3 πR³ where R is the radius of sphere. Find the rate of change of volume with respect to R.

Summary:

The volume of sphere is given by V = 4/3 πR³ where R is the radius of sphere. The rate of change of volume with respect to R is 4πR².