Question

teresa carved this solid out of wood. find the volume of the solid.

Explanation:

Step1: Calculate the volume of the left rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the left prism, \(l = 6\) in, \(w=4\) in, \(h = 8\) in. So \(V_1=6\times4\times8 = 192\) \(in^3\).

Step2: Calculate the volume of the middle rectangular prism

For the middle prism, \(l = 7\) in, \(w = 4\) in, \(h = 7\) in. So \(V_2=7\times4\times7=196\) \(in^3\).

Step3: Calculate the volume of the right rectangular prism

For the right prism, \(l = 6\) in, \(w = 4\) in, \(h = 8\) in. So \(V_3=6\times4\times8 = 192\) \(in^3\).

Step4: Calculate the total volume

The total volume \(V=V_1 + V_2+V_3\). Substitute the values: \(V=192 + 196+192\). \(V = 580\) \(in^3\).

Answer:

\(580\)