Question

what is the volume of this figure? 5 yd. 5 yd. 11 yd. 4 yd. 13 yd. cubic yards

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the L - shaped figure into two rectangular prisms. One prism has dimensions \(5\times5\times11\) and the other has dimensions \((13 - 5)\times4\times5\).

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 with \(l = 5\), \(w = 5\), and \(h = 11\), the volume \(V_1=5\times5\times11 = 275\) cubic yards.

Step3: Calculate the volume of the second prism

The second prism has \(l=(13 - 5)=8\), \(w = 4\), and \(h = 5\). Using the volume formula \(V = l\times w\times h\), we get \(V_2=8\times4\times5=160\) cubic yards.

Step4: Calculate the total volume

The total volume \(V = V_1+V_2\). So \(V=275 + 160=435\) cubic yards.

Answer:

435