Question

The volume of this rectangular prism is 288 cubic meters. What is the value of s?

s
12 m
12 m

s =
meters

Answer 1

To find the value of \( s \) for the rectangular prism with a volume of 288 cubic meters, we can use the formula for the volume of a rectangular prism:

\[
V = l \times w \times h
\]

where \( V \) is the volume, \( l \) is the length, \( w \) is the width, and \( h \) is the height.

In your case, you have dimensions given as \( s \) for two sides and 12 m for the third side. Assuming the sides are arranged such that \( l = s \), \( w = s \), and \( h = 12 \), then the volume can be expressed as:

\[
V = s \times s \times 12 = s^2 \times 12
\]

Given that the volume \( V = 288 \) cubic meters, we can set up the equation:

\[
s^2 \times 12 = 288
\]

Now, divide both sides by 12 to solve for \( s^2 \):

\[
s^2 = \frac{288}{12} = 24
\]

Next, take the square root of both sides to solve for \( s \):

\[
s = \sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}
\]

If you want a decimal approximation for \( s \):

\[
s \approx 2 \times 2.449 = 4.898
\]

Therefore, the value of \( s \) in exact form is \( 2\sqrt{6} \) meters, or approximately \( 4.90 \) meters.