​Calculate the volume of a square pyramid if it has base area of 64 cm2, and the distance from the apex to a corner of the base is 15cm

Length of each side of base = $+\sqrt{64}= 8$

Using Pyth. Thm., Slant height = $\sqrt{15^2-(\dfrac{8}{2})^2}=\sqrt{209}$

Using Pyth. Thm. again, Height = $\sqrt{(\sqrt{209})^2-(4)^2}=\sqrt{193}$

Volume = $\dfrac{1}{3}(8)^2(\sqrt{193})$

=$\dfrac{64\sqrt{193}}{3}\text{cm}^3$