Question

8 v= ________ cubic inches 18 in 3 in 8 in 8 in 4 in

Explanation:

Step1: Divide the shape into two rectangular - prisms

We can consider the L - shaped solid as two rectangular prisms. One prism has dimensions \(8\times8\times3\) and the other has dimensions \((18 - 8)\times8\times4\).

Step2: Calculate the volume of the first rectangular prism

The volume formula for a rectangular prism is \(V_1=l\times w\times h\). For the first prism with \(l = 8\) in, \(w = 8\) in, and \(h = 3\) in, we have \(V_1=8\times8\times3=192\) cubic inches.

Step3: Calculate the volume of the second rectangular prism

The length of the second prism is \(18−8 = 10\) in, width \(w = 8\) in, and height \(h = 4\) in. Using the volume formula \(V_2=l\times w\times h\), we get \(V_2=10\times8\times4 = 320\) cubic inches.

Step4: Calculate the total volume

The total volume \(V\) of the L - shaped solid is the sum of the volumes of the two prisms, \(V=V_1 + V_2\). So \(V=192+320=512\) cubic inches.

Answer:

512