Question

karen is moving into a new house. she has a lot of books that she wants to pack in small moving boxes. the dimensions of one of these moving boxes is shown below. image of a box labeled ( \frac{1}{4} ) m, ( \frac{2}{3} ) m, ( \frac{3}{4} ) m *picture not drawn to scale what is the volume of the small moving box? a. ( 1 \frac{2}{3} ) cu m b. ( \frac{1}{8} ) cu m c. ( \frac{6}{11} ) cu m d. ( \frac{1}{6} ) cu m

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism (which the box is) is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. From the diagram, the dimensions are \( \frac{1}{4} \, \text{m} \), \( \frac{2}{3} \, \text{m} \), and \( \frac{3}{4} \, \text{m} \).

Step2: Multiply the dimensions

Substitute the values into the formula:
\[
V=\frac{1}{4}\times\frac{2}{3}\times\frac{3}{4}
\]
First, multiply \( \frac{1}{4} \) and \( \frac{2}{3} \): \( \frac{1\times2}{4\times3}=\frac{2}{12}=\frac{1}{6} \). Then multiply the result by \( \frac{3}{4} \): \( \frac{1}{6}\times\frac{3}{4}=\frac{1\times3}{6\times4}=\frac{3}{24}=\frac{1}{8} \).

Answer:

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