Question

12\frac{1}{2} in. 2 in. 8 in. 16 in.^{3} 22\frac{1}{2} in.^{3} 200 in.^{3} 212\frac{1}{2} in.^{3}

Explanation:

Step1: Convert mixed number to improper fraction

\(12\frac{1}{2}=\frac{12\times2 + 1}{2}=\frac{25}{2}\)

Step2: Use the formula for the volume of a rectangular prism \(V = l\times w\times h\)

Here, \(l = 8\) in, \(w=2\) in, \(h=\frac{25}{2}\) in.
\(V=8\times2\times\frac{25}{2}\)
First, \(8\times2 = 16\)
Then, \(16\times\frac{25}{2}=\frac{16\times25}{2}\)
Since \(16\div2 = 8\), then \(8\times25=200\)

Answer:

\(200\) in.\(^{3}\)