Question

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

Step1: Split the figure into two rectangles

We can split the L - shaped figure into two rectangular prisms. The first one has dimensions \(l = 4\) in, \(w = 2\) in, \(h=(6 - 2)=4\) in. The second one has dimensions \(l = 10\) in, \(w = 2\) in, \(h = 2\) in.

Step2: Calculate the volume of the first prism

The formula for the volume of a rectangular prism is \(V=l\times w\times h\). For the first prism, \(l = 4\), \(w = 2\), \(h = 4\). So \(V_1=4\times2\times4 = 32\) cubic inches.

Step3: Calculate the volume of the second prism

For the second prism, \(l = 10\), \(w = 2\), \(h = 2\). Using the volume formula \(V=l\times w\times h\), we get \(V_2 = 10\times2\times2=40\) cubic inches.

Step4: Sum the volumes of the two prisms

To find the total volume of the figure, we add the volumes of the two prisms. \(V = V_1+V_2=32 + 40=72\) cubic inches.

Answer:

72