Question

samantha stores all of her important paperwork in the file cabinet shown below.
what is the volume of the file cabinet?
a. $6\frac{1}{12}$ cu ft
b. $4\frac{1}{36}$ cu ft
c. $7\frac{2}{9}$ cu ft
d. $2\frac{17}{24}$ cu ft

Explanation:

Step1: Convert mixed numbers to improper fractions

The formula for the volume of a rectangular prism is \(V = l\times w\times h\).
The length \(l = 2\frac{1}{6}=\frac{2\times6 + 1}{6}=\frac{13}{6}\), the width \(w=1\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4}\), and the height \(h = 2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}\).

Step2: Calculate the volume

\(V=\frac{13}{6}\times\frac{5}{4}\times\frac{8}{3}\).
First, multiply \(\frac{5}{4}\times\frac{8}{3}=\frac{5\times8}{4\times3}=\frac{40}{12}=\frac{10}{3}\).
Then, multiply \(\frac{13}{6}\times\frac{10}{3}=\frac{13\times10}{6\times3}=\frac{130}{18}=\frac{65}{9}=7\frac{2}{9}\).

Answer:

C. \(7\frac{2}{9}\text{ cu ft}\)