Question

of a rectangular prism are \\(\frac{9}{4}\\) feet, \\(3\frac{2}{3}\\) feet and \\(1\frac{1}{11}\\) feet respectively. what is

Explanation:

The problem seems to be about finding the volume of a rectangular prism (though the question part is cut off, but typically with length, width, height given, we find volume). The formula for the volume \( V \) of a rectangular prism is \( V = l\times w\times h \), where \( l \), \( w \), and \( h \) are the length, width, and height respectively.

Given:

• \( l=\frac{9}{4} \) feet
• \( w = 3\frac{2}{3}=\frac{3\times3 + 2}{3}=\frac{11}{3} \) feet
• \( h=1\frac{1}{11}=\frac{1\times11+ 1}{11}=\frac{12}{11} \) feet

Step 1: Multiply the first two dimensions

First, multiply \( \frac{9}{4} \) and \( \frac{11}{3} \).
\( \frac{9}{4}\times\frac{11}{3}=\frac{9\times11}{4\times3}=\frac{99}{12}=\frac{33}{4} \) (we simplify by dividing numerator and denominator by 3: \( \frac{99\div3}{12\div3}=\frac{33}{4} \))

Step 2: Multiply the result by the third dimension

Now, multiply \( \frac{33}{4} \) by \( \frac{12}{11} \).
\( \frac{33}{4}\times\frac{12}{11}=\frac{33\times12}{4\times11} \)
We can simplify before multiplying: 33 and 11 have a common factor of 11 (\( 33\div11 = 3 \), \( 11\div11=1 \)), and 12 and 4 have a common factor of 4 (\( 12\div4 = 3 \), \( 4\div4 = 1 \)).
So, \( \frac{3\times3}{1\times1}=9 \)

Step1: Convert mixed numbers to improper fractions

\( 3\frac{2}{3}=\frac{11}{3} \), \( 1\frac{1}{11}=\frac{12}{11} \)

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

\( V=\frac{9}{4}\times\frac{11}{3}\times\frac{12}{11} \)

Step3: Simplify and multiply

First, \( \frac{9}{4}\times\frac{11}{3}=\frac{33}{4} \), then \( \frac{33}{4}\times\frac{12}{11}=9 \)

Answer:

The volume of the rectangular prism is \( \boldsymbol{9} \) cubic feet.