Question

1. rectangular prism diagram ( 1 \frac{2}{3} ) in, ( \frac{1}{4} ) in, ( \frac{3}{5} ) in 2)

Explanation:

Assuming the problem is to find the volume of the rectangular prism (since it's a rectangular box with length, width, height given), we use the formula for the volume of a rectangular prism: \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step1: Convert mixed number to improper fraction

The length is \( 1\frac{2}{3} \) in. Convert it to an improper fraction: \( 1\frac{2}{3}=\frac{1\times3 + 2}{3}=\frac{5}{3} \)

Step2: Identify the dimensions

Length \( l=\frac{5}{3} \) in, width \( w = \frac{1}{4} \) in, height \( h=\frac{3}{5} \) in.

Step3: Multiply the dimensions

Using the volume formula \( V=l\times w\times h \), substitute the values:
\( V=\frac{5}{3}\times\frac{1}{4}\times\frac{3}{5} \)
First, multiply \( \frac{5}{3} \) and \( \frac{3}{5} \): \( \frac{5}{3}\times\frac{3}{5} = 1 \) (since numerator and denominator cancel out)
Then multiply the result by \( \frac{1}{4} \): \( 1\times\frac{1}{4}=\frac{1}{4} \)

Answer:

The volume of the rectangular prism is \( \frac{1}{4} \) cubic inches.