A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft.
What is the volume, in cubic feet, of space the tent occupies?
The diagram above comprises of a square base pyramid (at the top) and a square base prims (below).
Thus, the total volume = Volume of pyramid + Volume of prism
Volume of pyramid = 1/3 x Ah
Where A and h are the base area and height of the pyramid respectively.
Since the base is a square, A = Length x Width
A = 8 x 8 = 64
Therefore, Volume of pyramid = 1/3 x 64 x 3
Volume of prims = L x W x H
Where L, W and H are the Length, Width and Hight of the square base prism respectively
Volume of prism = 8 x 8 x 9
Thus, total volume = 64 + 576