More word problem help

[VP1]

So my question is-

A fire has started in a dry open field and is spreading in the form of a circle. If the radius of this circle increases at the rate of 6 feet/ minute express the total area A as a function of time t (in minutes).

It seems to me that area would = time(6(pi)time^2)
The answer in the book says the answer is= 36(pi)time^2

It is not clear to me why the 6 must be squared.
Help?

 

[tkhunny]

I'm a little puzzled why 't' was defined but never used. The variable "time" is quite cumbersone.

Radius(t) = t*(6 ft/min)

$\displaystyle Area(t)\;=\;\pi\cdot\left[Radius(t)\right]^{2}\;=\;??$

Are you seeing it, yet?

 

[soroban]

Hello, VP1!

A fire has started in a dry open field and is spreading in the form of a circle.
If the radius of this circle increases at the rate of 6 feet/minute, express the total area $\displaystyle A$ as a function of time $\displaystyle t$ (in minutes).

It seems to me that area would be: $\displaystyle A \,=\, 6\pi t^2$

The answer in the book says the answer is: $\displaystyle 36\pi t^2$

It is not clear to me why the 6 must be squared.

We are told that the radius is a function of time: .$\displaystyle r \,=\,6t$

$\displaystyle \text{Therefore: }\;A \;=\;\pi r^2 \;=\;\pi(6t)^2 \;=\;36\pi t^2$

 

[VP1]

Thanks for the quick help. That makes so much sense when it's explained, I just can't see it sometimes when looking at the question.

I definitely need to do more work with word problems to get more comfortable with them. Does anyone have any good websites that devote some reading to solving word problems?

Thanks- Todd

 

[tkhunny]

The most important work and pratice you can do is learning to WRITE clear and concise definitions at the beginning.