Final answer:
The height of the wall is 6 meters. The volume of space inside the tent can be found by calculating the volume of the cylindrical wall and the conical roof separately and then adding them together.
Step-by-step explanation:
Given that the radius of the tent is 9 meters and that the cylindrical wall and conical roof have the same height, let's denote the height of the wall as h.
a) To find the height of the wall, we can use the Pythagorean theorem.
The slant height of the cone is the hypotenuse of a right triangle formed by the height of the wall and the radius of the tent.
Using the formula r^2 + h^2 = l^2, we have 9^2 + h^2 = (9+h)^2. Expanding and simplifying this equation, we get h = 6.
b) To find the volume of space inside the tent, we need to calculate the volume of the cylindrical wall and the volume of the conical roof and then add them together.
The volume of the cylinder is given by V_cylinder = πr^2h = π(9^2)(6). The volume of the cone is given by V_cone = 1/3πr^2h = 1/3π(9^2)(6).
Adding these two volumes, we get the total volume of the space inside the tent.