West High School has a math building in the shape of a regular polygon. When Mrs. Woods measured an interior angle of the polygon (which was inside her classroom), she got $135°$.  

1. How many sides does the math building have? Show how you got your answer.

   Hint (a):

   Draw a diagram. What does it show? Refer to Math Note Box 8.1.5 for the formula for calculating the interior angle of a polygon.

   Answer (a):

   The building has $8$ sides.

2. If Mrs. Wood’s ceiling is $10$ feet high and the length of one side of the building is $25$ feet, find the volume of West High School’s math building.