Final answer:
To find the volume of the square pyramid, we need to find the height first using the Pythagorean theorem. Then we can use the volume formula V = (1/3)Bh, where B is the base area and h is the height. The base area can be calculated from the surface area of the pyramid.
Step-by-step explanation:
To find the volume of a square pyramid, we can use the formula V = (1/3)Bh, where B is the base area and h is the height. In this case, the slant height is given, so we need to find the height before we can calculate the volume. The slant height forms a right triangle with the height and half the base. Using the Pythagorean theorem, we can find the height: h^2 + (1/2)^2 = 17^2. Solving for h, we get h = sqrt(17^2 - (1/2)^2). Once we have the height, we can substitute the values into the volume formula: V = (1/3) x (base area) x h. The base area can be calculated using the surface area: 800 = (base area) + (4 x (1/2) x (1/2)), since a square pyramid has 4 triangular faces. Simplifying the equation, we get (base area) = 800 - (2 x (1/2) x (1/2)). Plug in the values and calculate the volume.