Question

find the volume of the solid below. 6 cm 6 cm 7 cm 4 cm 5 cm 13 cm

Explanation:

Step1: Calculate the volume of the first rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\).
For the first prism (left - hand side), \(l = 6\space cm\), \(w=5\space cm\), \(h = 6\space cm\).
\(V_1=6\times5\times6 = 180\space cm^3\)

Step2: Calculate the length of the second rectangular prism

The total length of the combined solid is \(13\space cm\), and one part has a length of \(6\space cm\). So the length of the second prism \(l_2=13 - 6=7\space cm\), \(w = 5\space cm\), \(h = 4\space cm\)

Step3: Calculate the volume of the second rectangular prism

Using the volume formula \(V = l\times w\times h\), for the second prism \(V_2=7\times5\times4=140\space cm^3\)

Step4: Calculate the total volume

The total volume \(V = V_1+V_2\)
\(V=180 + 140=320\space cm^3\)

Answer:

\(320\space cm^3\)