Volume of Rectangular Box

The areas of the sides of a rectangular box are 24, 32, and 48\;cm^2.

What is the volume of this box?
Source: NCTM Mathematics Teacher

SOLUTION

Let a,b,c represent the lengths of the sides.
ab=24\qquad\left (1\right )
ac=32\qquad\left (2\right )
bc=48\qquad\left (3\right )
Eqs. \left (1\right ) and \left (3\right ) yield
\frac{ab}{bc}=\frac{24}{48}
Simplify
\frac{a}{c}=\frac{1}{2}
Cross multiply
c=2a
Substitute the value of c into Eq. \left (2\right )
a\left (2a\right )=32
2a^2=32
a^2=16
a=4
Volume of box
bc=48
abc=a\times 48
=4\times 48
=192

Answer: 192\;cm^3

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About mvtrinh

Retired high school math teacher.
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