#### To determine

**To describe:** The representation of the derivatives dVdr and dVdt when the volume of the balloon V(t), radius is r(t) and time is *t.*

#### Explanation

The derivative dVdr represents the rate of change of the volume with respect to radius.

The derivative dVdt represents the rate of change of the volume with respect to time.

#### To determine

**To Express:** The derivative dVdt in terms of drdt.

#### Answer

The derivative dVdt can be expressed in terms of drdt is 4πr2drdt.

#### Explanation

**Formula used:**

The volume of the Sphere is V=4πr33.

**Calculation:**

The volume of the spherical weather balloon is V=4πr33.

Differentiate with respect to t,

dVdt=ddt(4πr33)=4π3ddt(r3)=4π3(3r3−1drdt) (Q ddx[g(x)]n=n[g(x)]n−1⋅g′(x))=4πr2drdt

Therefore, the derivative dVdt can be expressed in terms of drdt is dVdt=4πr2drdt.