SOLUTION: Hello, I have this question on a past paper for my exams which I am struggling with; "A gourmet chef is renowned for her spherical shaped souffle. Once it's put in the oven, its

Algebra ->  Bodies-in-space -> SOLUTION: Hello, I have this question on a past paper for my exams which I am struggling with; "A gourmet chef is renowned for her spherical shaped souffle. Once it's put in the oven, its      Log On


   

Question 601881: Hello, I have this question on a past paper for my exams which I am struggling with;
"A gourmet chef is renowned for her spherical shaped souffle. Once it's put in the oven, its volume increases at a rate proportional to its radius.
Show that the radius r cm of the souffle, at time t minutes after it has been put in the over, satisfies the differential equation dr%2Fdt=k%2Fr where k is constant."
Thank you :)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
"its volume increases at a rate proportional to its radius"

Therefore, where C is a constant. However we also know that



because the souffle is shaped like a sphere. Substitute into the first equation to obtain



Solve for dr/dt

(k is another constant).