Question

andrew is going camping this weekend. he purchased the ice chest below to hold his drinks.
image of ice chest with dimensions ( 1\frac{1}{2} ) ft, ( \frac{4}{5} ) ft, ( 1\frac{2}{3} ) ft, picture not drawn to scale
what is the volume of his ice chest?
a. ( 2 ) cu ft
b. ( 1 \frac{1}{6} ) cu ft
c. ( 3 \frac{29}{30} ) cu ft
d. ( 1 \frac{4}{15} ) cu ft

Explanation:

Step1: Convert mixed numbers to improper fractions

The dimensions of the ice chest (a rectangular prism) are \(1\frac{1}{2}\) ft, \(\frac{4}{5}\) ft, and \(1\frac{2}{3}\) ft.

• \(1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2}\)
• \(1\frac{2}{3}=\frac{1\times3+2}{3}=\frac{5}{3}\)

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

Substitute the values into the formula:
\(V=\frac{3}{2}\times\frac{4}{5}\times\frac{5}{3}\)

Step3: Simplify the multiplication

First, multiply \(\frac{3}{2}\) and \(\frac{4}{5}\): \(\frac{3}{2}\times\frac{4}{5}=\frac{3\times4}{2\times5}=\frac{12}{10}=\frac{6}{5}\)
Then, multiply \(\frac{6}{5}\) by \(\frac{5}{3}\): \(\frac{6}{5}\times\frac{5}{3}=\frac{6\times5}{5\times3}=\frac{30}{15} = 2\)

Answer:

A. 2 cu ft