Question

what is the volume of the small moving box?
a. $\frac{1}{6}$ cu m
b. $\frac{9}{11}$ cu m
c. $\frac{1}{8}$ cu m
d. $1\frac{2}{3}$ cu m

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Step2: Substitute the given values into the formula

Here, \(l=\frac{1}{4}\text{ m}\), \(w = \frac{2}{3}\text{ m}\), and \(h=\frac{3}{4}\text{ m}\). So \(V=\frac{1}{4}\times\frac{2}{3}\times\frac{3}{4}\).

Step3: Multiply the fractions

First, \(\frac{1}{4}\times\frac{2}{3}=\frac{1\times2}{4\times3}=\frac{2}{12}=\frac{1}{6}\). Then \(\frac{1}{6}\times\frac{3}{4}=\frac{1\times3}{6\times4}=\frac{3}{24}=\frac{1}{8}\).

Answer:

C. \(\frac{1}{8}\) cu m