Three faces of a right rectangular prism have areas of 48, 49 and 50 square units. What is the volume of the prism, in cubic units? Express your answer to the nearest whole number.

thx

Guest Jul 7, 2020

#1**0 **

Let's assign variables to each side length of the prism. Let's call them \(a\), \(b\), and \(c\).

We know the area of three of the faces, so let's write equations for that.

\(ab = 48\)

\(ac = 49\)

\(bc = 50\)

Now, let's multiply all our equations together. We get

\(a^2b^2c^c = 117600\).

Since we want to find the volume of the prism, we have to find \(abc\), so let's square root both sides of our equation.

\(abc=140\sqrt6\)

We want to round to the nearest whole number, so our answer is \(\boxed{343}\).

Guest Jul 7, 2020