Answer: The volume of the pyramid is (B) 48 ft³.
Step-by-step explanation: We are given to find the volume of the pyramid shown in the figure.
The VOLUME of a pyramid with base area 'b' square units and height 'h' units is given by
[tex]V=\dfrac{1}{3}bh.[/tex]
Here, the base is a square with side of length 6 ft, so the area of the base, 'b' is given by
[tex]b=6\times 6=36~\textup{square units}.[/tex]
Now, as shown in the modified attached figure, ABC is a right-angles triangle at ∠B, and AC is the slanting height of 5 ft.
AB is the height of the pyramid.
BC is equal to half of the side length of the square base, so we have
[tex]BC=\dfrac{6}{2}=3~\textup{ft}.[/tex]
Now, using Pythagoras Theorem, we have
[tex]AC^2=AB^2+BC^2\\\\\Rightarrow AB^2=AC^2-BC^2\\\\\Rightarrow AB=\sqrt{5^2-3^2}\\\\\Rightarrow AB=\sqrt{16}\\\\\Rightarrow AB=4~\textup{ft}.[/tex]
Hence, height of the pyramid, h = 4 ft.
Therefore, the volume of the Pyramid will be
[tex]V=\dfrac{1}{2}\times bh=\dfrac{1}{3}\times 36\times 4=48~\textup{ft}^3.[/tex]
Thus, the volume of the pyramid is 48 ft³.
Option (B) is correct.
