First of all, we need to establish some known things. Let us call the radius r and the center of the circle R. Consider RD and then consider the 2 triangles DUR and DSR. We have that they have both a 90 degree angle (due to the tangency condition), they have DR common and also SR is equal to UR since both are equal to r. Hence, we have that the triangles are equal, thus, we have that DS=DU. Since DF=DU+UF, we have that DF=11
In a circle inscribed within a triangle, the distance from each vertex of the triangle to the two nearest touchpoints (points of tangency on the circle) are equal. Since SD=4, DT=4 as well. Since UF=7, then FT=7.
In this question, you are given the width( 20 miles), the length(28 miles) and the height( 1 inch). You are asked to count the rain water volume which was going with formula length x width x height. But the unit asked is ft, so you need to convert them all. The calculation would be:
Water volume= length x width x height Water volume= 20 miles x 5280ft/miles x 28 miles x 5280ft/miles x 1inch x 1ft/12inch Water volume = 1300992000 cubic ft.
