Environmental Impact A chemical company has a failure in one oftheir processing plants that startsto release a dangerous chemical into the air. The chemical is denser than airso it stays close to the ground as it expands. The local interstate has an exit 20 miles west and 5 miles south of the plant and there's a small town 30 miles north and 2 miles east ofthe plant. The interstate is the quickest evacuation root for the town. Draw a map ol the scenario piclting an appropriate location for the origin and axes and indicating all of the relevant locations. The chemical is being released at a rate of 50 liters per second. If you assume that the gas is expanding in a spherical shape, how fast is the radius of the sphere increasing, i.e. what is drfdt? What happens to the rate of change of the radius as the radius increases? Based on your calculations, howI fast is the radius ol the cloud increasing when it reaches the town and the interstate exit? Another model of the gases behavior assumes that it will expand up faster than it expands out. This happens because, as the gas gets higher, air pressure gets lower which lets the gas expand up faster. At ground level, the shape of the cloud will still be a circle but it will be stretched in the \"up\" direction. If the radius at the base is r and the height of the cloud is h then the volume will be V: in!!! .lr \"'0". Using this expression, how fast is the radius of the circle Assume that the height is equal to r -l on the ground increasing? Based on your calculations, how fast is the radius of the cloud increasing when it reaches the town and the interstate exit