Question

what is the volume of this figure? cubic feet 8 ft. 2 ft. 4 ft. 5 ft. 2 ft.

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given figure into two rectangular - prisms. One with dimensions \(8\) ft (length), \(4\) ft (width), \(2\) ft (height) and another with dimensions \(2\) ft (length), \(4\) ft (width), \((5 - 2)=3\) ft (height).

Step2: Calculate the volume of the first rectangular - prism

The volume formula for a rectangular - prism is \(V = l\times w\times h\). For the first prism with \(l = 8\) ft, \(w = 4\) ft, \(h = 2\) ft, we have \(V_1=8\times4\times2=64\) cubic feet.

Step3: Calculate the volume of the second rectangular - prism

For the second prism with \(l = 2\) ft, \(w = 4\) ft, \(h = 3\) ft, using the volume formula \(V = l\times w\times h\), we get \(V_2=2\times4\times3 = 24\) cubic feet.

Step4: Calculate the total volume

The total volume \(V\) of the figure is the sum of the volumes of the two prisms, \(V=V_1 + V_2\). So \(V=64+24 = 88\) cubic feet.

Answer:

88