Question

the three - dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. find the volume of the solid in cubic centimeters. 180 cubic centimeters 580 cubic centimeters 500 cubic centimeters 420 cubic centimeters

Explanation:

Step1: Calculate the volume of the large rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the large prism, \(l = 20\) cm, \(w = 5\) cm, \(h = 5\) cm. So \(V_{large}=20\times5\times5= 500\) \(cm^{3}\).

Step2: Calculate the volume of the small rectangular - prism (hole)

For the small prism (hole), \(l = 20\) cm, \(w = 2\) cm, \(h = 2\) cm. Using the volume formula \(V=l\times w\times h\), we get \(V_{small}=20\times2\times2 = 80\) \(cm^{3}\).

Step3: Calculate the volume of the solid

The volume of the solid \(V = V_{large}-V_{small}\). Substitute the values: \(V=500 - 80=420\) \(cm^{3}\).

Answer:

420 cubic centimeters