When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
The choices:
- $\frac{\sqrt{10}}{2}$
- $\sqrt{10}$
- 4
- 5
- 10
So I started off with this.
The rate is 22 $m^3$/hr and so after 1 hour, there will be 22 $m^3$ in the tanka and the height will be 0.7m
So...
22 = $\pi$ * $r^2$ * 7/10
$\frac {220}{7}$ = $\pi$ * $r^2$
Now what?
You probably know that $\frac{22}7$ is approximately $\pi$, so your last equation is approximately $10\pi=\pi r^2$; now just cancel $\pi$.