Question

a new dictionary in the shape of a rectangular prism will have a thickness of 3 inches (in). the volume of the dictionary will be 216 in³. what must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is \( V = A\times h \), where \( A \) is the area of the base (in this case, the area of the front - cover which is perpendicular to the thickness) and \( h \) is the height (thickness in this problem).

Step2: Solve for the area \( A \)

We know that \( V = 216\space in^{3}\) and \( h=3\space in\). Rearranging the formula \( V = A\times h\) for \( A\), we get \( A=\frac{V}{h}\).
Substitute \( V = 216\) and \( h = 3\) into the formula: \( A=\frac{216}{3}\).

Answer:

\( 72 \)