A spherical raindrop evaporates at a rate proportional to its surface area. Write down a differ- ential equation for its volume as a function as a function of time. Solve this equation, and find the constant of proportionality if a 1cm3 raindrop takes 10 seconds to evaporate.

k = 3.022

Step-by-step explanation:

Given that:

A spherical raindrop evaporates at a rate proportional to its surface area.

The surface area SA of a spherical object is given by the relation:

SA = 4πr²

Write down a differ- ential equation for its volume as a function as a function of time.

So; to differentiate Volume (V) in respect to time (t) ;then:

Likewise; we know known that the volume of a sphere V =

Thus, from above;

Thus; solving the differential:

So;

we are to find the constant proportionality K

If Volume V = 1 cm³ and the time = 10 sec

0.1 =  - 4π k (0.3848 × 1)

0.1 =  - 4π k × 0.3848

4π k = 0.3848/0.1

4π k  = 3.848

k = 3.848/4π

k = 3.022

correct answer:

b.(19,-2)