A spherical snowball is melting in such a way that its surface area decreases at a rate of . How fast is its radius shrinking when it is ?

Question

A spherical snowball is melting in such a way that its surface area decreases at a rate of  . How fast is its radius shrinking when it is  ?

Trinidad · Accepted Answer

The surface area of the spherical snowball has a formula 
    
Where
 radius of the spherical snowball
 
Differentiating the formula with respect to time  and applying Chain Rule, we get
  
 
Given the following information
    
  
We can now evaluate the unknown variable as follows
    
 
Hence, the radius is shrinking at a rate of

A spherical snowball is melting in such a way that its surface area decreases at a rate of . How fast is its radius shrinking when it is ?

Unlock this answer

Unlock this answer