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. 48 cubic centimeters 96 cubic centimeters 120 cubic centimeters 108 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, \(l = 12\) cm, \(w=3\) cm, \(h = 3\) cm. So \(V_{large}=12\times3\times3=108\) \(cm^{3}\).

Step2: Calculate the volume of the hole

The hole is also a rectangular prism. Its dimensions: \(l = 12\) cm, \(w = 1\) cm, \(h = 1\) cm. Using the volume formula \(V=l\times w\times h\), we get \(V_{hole}=12\times1\times1 = 12\) \(cm^{3}\).

Step3: Calculate the volume of the solid

Subtract the volume of the hole from the volume of the large prism. \(V = V_{large}-V_{hole}\). So \(V=108 - 12=96\) \(cm^{3}\).

Answer:

96 cubic centimeters