#### To determine

**(a)**

**To find:** The rate of change of the volume with respect to the height if the radius is constant

#### Answer

**dVdh=13πr2**

#### Explanation

By differentiating volume of cone with respect to h using differentiation rules

**1) Formula:**

(i) Constant multiple rule:

ddxCf(x)=Cddx(fx)

**2) Given:**

V=13πr2h

**3) Calculation:**

Consider the function,

V=13πr2h

To find rate of change of the volume with respect to the height differentiate function with respect to h,

dVdh=ddh(13πr2h)

By using constant multiple rule,

dVdh=13πr2ddh(h)

⇒dVdh=13πr2

**Final statement:**

dVdh=13πr2

#### To determine

**(b)**

**To find:**The rate of change of the volume with respect to the radius if the height is constant

#### Answer

**dVdr=23πhr**

#### Explanation

By differentiating volume of cone with respect to r using differentiation rules

**1) Formula:**

i. Power rule:

ddxxn=nxn-1

ii. Constant multiple rule:

ddxCf(x)=Cddx(fx)

**2) Given:**

V=13πr2h

**3) Calculation:**

Consider the function, V=13πr2h

To find rate of change of the volume with respect to the radius differentiate function with respect to r,

dVdr=ddh(13πr2h)

By using constant multiple rule,

dVdr=13πhddr(r2)

dVdr=23πhr

**Final statement:**

dVdr=23πhr