show in the notation of the figure that the volume of the gasoline that fills the tank to depth d is
V= 2L integral {-r , -r+d} sqrt (r^2 - y^2)dy
how can i show that ?
Let R=radius of tank and d=depth of gas.
The circle that makes up the ends of the tank can be represented by
Integrate this over the depth of the gas.
Multiply by L for the length of the tank and multiply by 2 to include the whole circle and not just the upper portion.