Rita is designing a building shaped like a pyramid that's cut off in a plane parallel to its base (this is called a truncated pyramid).The building has a 64 × 64 m square base and is 36 m tall. The cut off section has a 16 × 16 m, square base and is 12 m tall. What is the volume of the buliding?

48,128 m³

Step-by-step explanation:

The volume of the full shape is that of a pyramid. So the volume is V = Ah/3 where A = area of base and h = height.

Now for the full shape A = 64 m × 64 m and h = 36 m.

So, V = Ah/3 = 64 m × 64 m × 36 m/3 =  64 m × 64 m × 12 m = 49,152 m³

The volume of the cut section is V' = A'h'/3 since it is also a pyramid. Where  A' = area of base and h' = height.

For the cut section A' = 16 m × 16 m and h' = 12 m

So, V' = A'h'/3 = 16 m × 16 m × 12 m/3 = 16 m × 16 m × 4 m = 1,024 m³.

So, the volume of Rita's building is the difference between the volumes of the two sections.

So, the volume of Rita's building is V" = V - V' = 49,152 m³ - 1,024 m³ = 48,128 m³