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 \( \frac{2}{3} \) ft. First, convert \( 1\frac{1}{2} \) to an improper fraction: \( 1\frac{1}{2}=\frac{3}{2} \).

Step2: Use the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l\times w\times h \), where \( l \), \( w \), and \( h \) are the length, width, and height respectively. Substitute the values: \( V=\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3} \).

Step3: Multiply the fractions

First, multiply \( \frac{3}{2} \) and \( \frac{4}{5} \): \( \frac{3}{2}\times\frac{4}{5}=\frac{12}{10}=\frac{6}{5} \). Then multiply the result by \( \frac{2}{3} \): \( \frac{6}{5}\times\frac{2}{3}=\frac{12}{15}=\frac{4}{5} \)? Wait, no, wait. Wait, let's do it step by step correctly. Wait, \( \frac{3}{2}\times\frac{4}{5}\times\frac{2}{3} \). We can cancel common factors. The 3 in the numerator of the first fraction and the 3 in the denominator of the third fraction cancel. The 2 in the numerator of the third fraction and the 2 in the denominator of the first fraction cancel. So we have \( \frac{1}{1}\times\frac{4}{5}\times\frac{1}{1}=\frac{4}{5} \)? No, that's not right. Wait, maybe I messed up the dimensions. Wait, the dimensions are \( 1\frac{1}{2} \) (length), \( \frac{4}{5} \) (width), and \( \frac{2}{3} \) (height)? Wait, no, maybe the height is \( \frac{2}{3} \), length \( 1\frac{1}{2} \), width \( \frac{4}{5} \). Wait, let's recalculate:

\( 1\frac{1}{2}=\frac{3}{2} \), so \( \frac{3}{2} \times \frac{4}{5} \times \frac{2}{3} \). Multiply numerators: \( 3\times4\times2 = 24 \). Multiply denominators: \( 2\times5\times3 = 30 \). So \( \frac{24}{30} \), simplify by dividing numerator and denominator by 6: \( \frac{4}{5} \)? But that's not one of the options. Wait, maybe I got the dimensions wrong. Wait, maybe the height is \( 1\frac{2}{3} \)? Wait, the diagram shows \( 1\frac{2}{3} \) ft? Wait, the user's diagram: "1 1/2 ft", "4/5 ft", and "1 2/3 ft"? Wait, maybe I misread the height. Let me check again. The problem says: the ice chest has dimensions \( 1\frac{1}{2} \) ft, \( \frac{4}{5} \) ft, and \( 1\frac{2}{3} \) ft? Wait, maybe the original problem has a typo or my misreading. Wait, the options include \( 3\frac{29}{30} \), \( 1\frac{4}{15} \), etc. Let's re-express the dimensions correctly. Let's assume the dimensions are \( 1\frac{1}{2} \) (length), \( \frac{4}{5} \) (width), and \( 1\frac{2}{3} \) (height). Then:

\( 1\frac{1}{2}=\frac{3}{2} \), \( 1\frac{2}{3}=\frac{5}{3} \). Then volume \( V = \frac{3}{2} \times \frac{4}{5} \times \frac{5}{3} \). Let's calculate:

\( \frac{3}{2} \times \frac{4}{5} = \frac{12}{10} = \frac{6}{5} \). Then \( \frac{6}{5} \times \frac{5}{3} = \frac{30}{15} = 2 \). Oh! So maybe the height is \( 1\frac{2}{3} \) instead of \( \frac{2}{3} \). That must be my mistake. So let's correct the dimensions: length \( 1\frac{1}{2} = \frac{3}{2} \), width \( \frac{4}{5} \), height \( 1\frac{2}{3} = \frac{5}{3} \).

Step1: Convert mixed numbers to improper fractions

\( 1\frac{1}{2} = \frac{3}{2} \), \( 1\frac{2}{3} = \frac{5}{3} \).

Step2: Apply volume formula \( V = l \times w \times h \)

\( V = \frac{3}{2} \times \frac{4}{5} \times \frac{5}{3} \).

Step3: Simplify the product

Notice that \( \frac{3}{2} \times \frac{5}{3} = \frac{15}{6} = \frac{5}{2} \), then \( \frac{5}{2} \times \frac{4}{5} = \frac{20}{10} = 2 \). Alternatively, cancel common factors: the 3 in the numerator of the first fraction and the 3 in the denominator of the third fraction cancel. The 5 in the numerator of the third fraction and the 5 in the denominator of the second fraction cancel. The 4 in the numerator of the second fraction and the 2 in the denominator of the first fraction: 4 divided by 2 is 2. So we have \( 1 \times 2 \times 1 = 2 \).

Answer:

A. 2 cu ft