8) a regular square pvamid with base edge length 12 ft and slant hoight 10 ft

To find the volume of a regular square pyramid, we can use the formula: \[ V = \frac{1}{3}Bh \] where: - \( V \) is the volume of the pyramid, - \( B \) is the area of the base of the pyramid, and - \( h \) is the height of the pyramid. Given: - Base edge length = 12 ft - Slant height = 10 ft First, we need to find the height of the pyramid. We can use the Pythagorean theorem to find the height: \[ h^2 + (\frac{12}{2})^2 = 10^2 \] Solving for \( h \): \[ h^2 + 6^2 = 10^2 \] \[ h^2 + 36 = 100 \] \[ h^2 = 100 - 36 \] \[ h^2 = 64 \] \[ h = \sqrt{64} \] \[ h = 8 \text{ ft} \] Now, we can find the volume of the pyramid: \[ V = \frac{1}{3}Bh \] \[ V = \frac{1}{3}(12^2)(8) \] \[ V = \frac{1}{3}(144)(8) \] \[ V = \frac{1}{3}(1152) \] \[ V = 384 \text{ ft}^3 \] Therefore, the volume of the regular square pyramid is 384 cubic feet.