find area of base of tank let us consider following problem:
When $30$ gallons water poured in to cylinder whose sides are perpendicular to base, water level rises $0.5$ ft, if $7.5$ gallons occupy $1$cu.ft space what is the area of base of tank?
so as i understand we have cylinder,which's  volume is equal to 
$\pi*r^2*h$
now  when we have poured $30$ gallon,then  water level rises $0.5$ ft,what does it means?does it means that it's  volume is increased by $0.5$  or height?also what i think  if $7.5$ gallon occupy volume of $1$cu.ft,which means that $\pi*r^2*h=1$,then how can i connect these two information together?can i say that $30$ gallon occupy $4$  cu.ft,because $30/7.5=4$,so it means that
$\pi*r^2*h=1$
$\pi*r^2*(h+0.5)=4$? if it is so then   i will got $\pi*r^2*0.5=3$ from which  $\pi*r^2=6$ is it correct?
 A: The $\pi r^2h=1$ is not true.  They mean that you can use the $30/7.5=4$ as you described such that:
$$\pi r^2(.5)=4$$
I think you understand this well enough to do the rest.  The initial height of water in the tank does not matter.
A: Not quite. $30$ gallons take up $4$ cubic feet of space, as you've determined, but the rest doesn't really make sense. You seem to be starting with one cubic foot of water in the tank, so when we pour in $30$ gallons ($4$ cubic feet), we have a change in water level of $0.5$ feet, yes, but our new volume of water is $5$ gallons. That is, if $$\pi r^2h=1,$$ then $$\pi r^2(h+0.5)=5,$$ whence $\pi r^2\cdot0.5=4,$ and you can solve from there.
More simply, we could just assume that we started with an empty tank and poured in $30$ gallons ($4$ cubic feet), so that our change in water level is exactly the water level. That is, $$\pi r^2\cdot0.5=4,$$ as before.
Edit: Instead of making such an assumption, let us instead assume that $V$ is the volume of water originally in the tank and $h$ is the initial water level (in feet). The cylindrical shape tells us that $$\pi r^2h=V,$$ where $r$ is the radius of the tank (in feet). The addition of $4$ cubic feet of water increases the water level by $0.5$ feet, meaning that $$\pi r^2(h+0.5)=V+4.$$ Once again, we find that $$\pi r^2\cdot0.5=4.$$
