During a typical afternoon thunderstorm in the summer, an area of 16.0 km^2 receives 2.82 10^8 gal of rain in 18 min. How many inches of rain fell during this 18 min period?

Answer 1

The problem is asking for the inches (in depth) that the area (16 km^2) received. If you picture the area like an open box, the area of the floor of the box is 16 km^2, and the height would be the "inches of rain" we are solving for.

We know that 10^8 gallons of rain fell in total, so if you imagine that the "box" can hold that much water (aka the volume of the box), we can take the volume and divide by the area of the floor to the get the height of the box (or the rain in inches). But we must make sure that we pay attention to our units.

First, let's convert gallons to km^3.

1 km^3 = 2.642 x 10^11

10^8 gallons = 3.785 x 10^-5 km^3

Taking the volume in km^3 and dividing by the area in km^2:

(3.785 x 10^-5 km^3) / (16 km^2) = 2.366 x 10^-5 km

Now we convert that number to inches

1 km = 39370.1 in

2.366 x 10^-5 km = 0.92 inches