#### To determine

**To show:**

The depth of the water decreases at a constant rate regardless of the shape of the bowl.

#### Answer

The depth of the water decreases at a constant rate regardless of the shape of the bowl.

#### Explanation

The rate of change of volume of water is given as

dVdt=-kAx ⋯(1)

where k is some positive constant and Ax is the area of the surface when the water has depth x.

The rate of change of the depth of water with respect to time is dxdt.

By the Chain rule,

dVdt=dVdxdxdt

From equation (1),

dVdt·dxdt=-kAx ⋯(2)

The total volume of water up to a depth x is

Vx=∫0xAsds

where As is the area of cross section of the water at depth s.

Differentiating this equation with respect to x,

dVdx=Ax

Substitute this in equation (2).

Axdxdt=-kA(x)

Dividing by Ax,

dxdt= -k

This is a constant.

That means, it does not depend on the shape of the bowl.

**Conclusion:**

The depth of the water decreases at a constant rate regardless of the shape of the bowl.