A matlab program needs to be written for the following problem:

Problem: A water tank supplies a tract of 5 homes. It is dimensioned below 50 m Frustum 35 m h = ht of water in Frustum r = radius of cylinder Cylinder R = radius of Frustum at h 40 m 36 m Scenario 1: The water tank shown has water to 55 m deep (15 m into the Frustum area) The homes consume 7K m3 per day. After 2 days what will be the new tank level? Scenario 2: The water tank shown has water to 45 m deep (5 m into the Frustum area) The homes consume 5K m3 per day. After 2 days what will be the new tank level? Method: First - Determine if new volume is still in frustum or not. If not the solution is very easy because it is the partial volume consumed in the cylinder Second - If the level is still in the frustum note that the Volume equations can be reduced to a single variable x which is the new difference between R and r for the new volume, this is the only unknown because h (while also an unknown) can be expressed as a function of x by proportional triangles. Therefore h can be expressed as a function of x, and R can be expressed as a function of x. Note r is a constant. Now you have a 3rd order polynomial that can be solved by the roots function. Left to the student to use the "help" in Matlab to discover how the function roots works Results: Volume initially in Tank Volume and height of water for Senario 1 Volume and height of water for Senario 2 Write this program as a script file (name.m) Problem: A water tank supplies a tract of 5 homes. It is dimensioned below 50 m Frustum 35 m h = ht of water in Frustum r = radius of cylinder Cylinder R = radius of Frustum at h 40 m 36 m Scenario 1: The water tank shown has water to 55 m deep (15 m into the Frustum area) The homes consume 7K m3 per day. After 2 days what will be the new tank level? Scenario 2: The water tank shown has water to 45 m deep (5 m into the Frustum area) The homes consume 5K m3 per day. After 2 days what will be the new tank level? Method: First - Determine if new volume is still in frustum or not. If not the solution is very easy because it is the partial volume consumed in the cylinder Second - If the level is still in the frustum note that the Volume equations can be reduced to a single variable x which is the new difference between R and r for the new volume, this is the only unknown because h (while also an unknown) can be expressed as a function of x by proportional triangles. Therefore h can be expressed as a function of x, and R can be expressed as a function of x. Note r is a constant. Now you have a 3rd order polynomial that can be solved by the roots function. Left to the student to use the "help" in Matlab to discover how the function roots works Results: Volume initially in Tank Volume and height of water for Senario 1 Volume and height of water for Senario 2 Write this program as a script file (name.m)