Question

A right rectangular prism with a square base is shown. Dimensions are given in units. The volume of the prism is 192 cubic units. What is the height, h, of the prism in units? The length is h and the width is 4.
A. 48 units
B. 12 units
C. 24 units
D. 64 units

Answer 1

To find the height \( h \) of the right rectangular prism, we can start by using the formula for the volume of a rectangular prism, which is given by:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

In this case, we know that:
- The volume is \( 192 \) cubic units.
- The length \( h \) is \( h \), and the width is \( 4 \).

Since the base of the prism is a square, the width will also be \( 4 \) units. Therefore, we can substitute these values into the volume formula:

\[
192 = 4 \times 4 \times h
\]

Now, simplify the equation:

\[
192 = 16h
\]

Next, we solve for \( h \) by dividing both sides by \( 16 \):

\[
h = \frac{192}{16}
\]

Calculating the right-hand side gives:

\[
h = 12
\]

Thus, the height \( h \) of the prism is \( \boxed{12} \) units.