Question

what is the volume of this figure? cubic yards

Explanation:

Step1: Divide figure into two rectangular - prisms

We can divide the given 3 - D figure into two rectangular prisms. One prism has dimensions \(12\times4\times2\) and the other has dimensions \(12\times(4 + 4)\times2\).

Step2: Calculate volume of first prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). For the first prism with \(l = 12\) yd, \(w = 4\) yd, and \(h = 2\) yd, \(V_1=12\times4\times2=96\) cubic yards.

Step3: Calculate volume of second prism

For the second prism with \(l = 12\) yd, \(w=(4 + 4)=8\) yd, and \(h = 2\) yd, \(V_2=12\times8\times2 = 192\) cubic yards.

Step4: Calculate total volume

The total volume \(V\) of the figure is \(V=V_1 + V_2\). So \(V=96+192 = 288\) cubic yards.

Answer:

288