1. ## word problem help

This problem has me stumped!
A stone dropped into a pond creates a circular ripple whose radius expands at the rate of 1.5 ft/sec. Assuming the initial radius of the circle is 0, find the number of square feet enclosed by the ripple after one minute.

Now, I know I have to use (pi)r^2. I'm just not sure where the 1.5 feet and 60 seconds would fit in.

2. Time 0 sec: pi(0 in)^2 = 0 in^2
Time 1 sec: pi(1.5 in)^2 = 2.25 pi in^2
Time 2 sec: pi(2*1.5 in)^2 = 9 pi in^2
Time 3 sec: pi(3*1.5 in)^2 = 20.25 pi in^2
...
Time 60 sec: pi(60*1.5 in)^2 = ???

Are you seeing it?

One more thing. This is in in^2. You must convert to ft^2. Do you know how to do that? It is NOT simply dividing by 12.

3. Originally Posted by TKHunny
Time 0 sec: pi(0 in)^2 = 0 in^2
Time 1 sec: pi(1.5 in)^2 = 2.25 pi in^2
Time 2 sec: pi(2*1.5 in)^2 = 9 pi in^2
Time 3 sec: pi(3*1.5 in)^2 = 20.25 pi in^2
...
Time 60 sec: pi(60*1.5 in)^2 = ???

Are you seeing it?

One more thing. This is in in^2. You must convert to ft^2. Do you know how to do that? It is NOT simply dividing by 12.
How would I be able to convert to ft^2? I understand at 60 seconds it would be 90 pi in^2. Would I have to square to 8100?

4. Originally Posted by lemon301
How would I be able to convert to ft^2? I understand at 60 seconds it would be 90 pi in^2. Would I have to square to 8100?
Factor-label method:
$\frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2$
gives you the conversion factor.

-Dan

5. Originally Posted by topsquark
Factor-label method:
$\frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2$
gives you the conversion factor.

-Dan
So do I have to divide 90 by 12? I understand the inches will cancel out but the 12 is throwing me off.

6. Originally Posted by lemon301
So do I have to divide 90 by 12? I understand the inches will cancel out but the 12 is throwing me off.
Look at that little 2 above the second factor. You have inches times inches, so you need to divide by two factors:
$\frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right )^2 = \frac{1~in^2}{1} \cdot \left ( \frac{1~ft}{12~in} \right ) \cdot \left ( \frac{1~ft}{12~in} \right )$

-Dan