Question

what is the volume of this figure? 2 in. 4 in. 6 in. 2 in. 10 in. cubic inches

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the L - shaped figure into two rectangular prisms. One prism has dimensions \(4\times2\times6\) and the other has dimensions \((10 - 4)\times2\times2\).

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 \(l = 4\) in, \(w = 2\) in, and \(h = 6\) in, \(V_1=4\times2\times6=48\) cubic inches.

Step3: Calculate the volume of the second prism

The length of the second prism is \(10 - 4=6\) in, width \(w = 2\) in, and height \(h = 2\) in. Using the volume formula \(V = l\times w\times h\), \(V_2=6\times2\times2 = 24\) cubic inches.

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 \(V=48+24 = 72\) cubic inches.

Answer:

72