Question

find the volume of the solid. diagram of a rectangular prism with dimensions 4 in, 7 in, 3 in the volume of the solid is \\(\square\\) (simplify your answer.) options: square inches, inches, cubic inches.

Explanation:

Step1: Recall the formula for the volume of a rectangular prism

The volume \( V \) of a rectangular prism (a box - shaped solid) is given by the formula \( V = l\times w\times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
From the diagram, we can see that the length \( l = 7\) in, the width \( w = 4\) in, and the height \( h = 3\) in.

Step2: Substitute the values into the formula

Substitute \( l = 7 \), \( w = 4 \), and \( h = 3 \) into the formula \( V=l\times w\times h \).
We get \( V=7\times4\times3 \).
First, calculate \( 7\times4 = 28 \). Then, calculate \( 28\times3=84 \).
Also, the unit of volume for a three - dimensional object is cubic units. Since the dimensions are in inches, the unit of volume is cubic inches.

Answer:

\( 84 \) cubic inches