Chain Rule/Differentiation

[KieranLWalker]

Hi, I am working through a question in MEI structured mathematics, third edition C3, exercise 4A question 8. I have been using the method outlined in the examples, and for the previous questions, my answers have been correct, but for this question my answer is similar but too large, so I think I have missed something, but am unable to see what it is. Here is the question:

The radius of a circular fungus is increasing at a uniform rate of 5cm per day. At what rate is the area increasing when the radius is 1m?

Here is my workings out:

A= pi*r2, dA/dr= 2*pi*r
dA/dt=2*pi*r*dr/dt
dA/dt=2*pi*r*5,dA/dt=2*pi*100*5
dA/dt=31.41592..m2 per day.

This I thought was right, but when checking my answer with the book, the book gave:
0.3141m2 per day to be the correct answer. Any help that you are able to give will be greatly appreciated. Thanks in advance!

 

[galactus]

Be careful of the units. It says 5 CM and the asks for the rate when the radius is 1 M

I think you just have the units entered in a little wrong. Your units are in cm, not meters.

5 cm = 1/20 m

\(\displaystyle \frac{dA}{dt}=2{\pi}(1)(\frac{1}{20})=\frac{\pi}{10} \;\ m^{2}\)

See now?.

Convert the other way:

\(\displaystyle 2{\pi}(100)(5)=1000{\pi} \;\ cm^{2}\)

Same thing because there are 10,000 cm^2 in 1 m^2

 

[KieranLWalker]

Ah thank you, yes I see now. I suppose I started to rush things as I neared the end of the exercise. A silly mistake, but thank you all the same.