Question

what is the volume of this figure? 1,125 cubic feet 750 cubic feet 1,000 cubic feet 875 cubic feet

Explanation:

Step1: Divide the figure into two rectangular - prisms.

The first prism has dimensions \(l = 15\) ft, \(w = 5\) ft, \(h = 10\) ft. The second prism has dimensions \(l=(15 + 5)\) ft, \(w = 5\) ft, \(h = 10\) ft.

Step2: Calculate the volume of the first prism.

The volume formula for a rectangular - prism is \(V=l\times w\times h\). For the first prism, \(V_1 = 15\times5\times10=750\) cubic feet.

Step3: Calculate the volume of the second prism.

For the second prism, \(l = 20\) ft, \(w = 5\) ft, \(h = 10\) ft. So \(V_2=20\times5\times10 = 1000\) cubic feet. But we made a wrong split. Let's split it another way.
Divide the figure into three rectangular - prisms.
The first prism: \(l = 5\) ft, \(w = 5\) ft, \(h = 10\) ft, \(V_1=5\times5\times10 = 250\) cubic feet.
The second prism: \(l=(15 - 5)\) ft, \(w = 5\) ft, \(h = 10\) ft, \(V_2 = 10\times5\times10=500\) cubic feet.
The third prism: \(l = 5\) ft, \(w = 5\) ft, \(h = 10\) ft, \(V_3=5\times5\times10 = 250\) cubic feet.

Step4: Calculate the total volume.

\(V=V_1 + V_2+V_3=250 + 500+250=1000\) cubic feet.

Answer:

1,000 cubic feet