Answer
$607\; pounds$.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the weight of the men be $W$
and the height be $H$.
Because $W$ varies directly by $H^3$ we have:
$\Rightarrow W=kH^3$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $W=170\; pounds$ and $H=70\; inches$.
Substitute into the equation (1).
$\Rightarrow 170=k(70)^3$
$\Rightarrow 170=343000k$
Divide both sides by $343000$.
$\Rightarrow \frac{170}{343000}=\frac{343000k}{343000}$
Simplify.
$\Rightarrow \frac{17}{34300}=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=\frac{17}{34300}$ into the equation (1).
$\Rightarrow W=\frac{17}{34300}H^3$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $H=107\;inches$ into the equation (2).
$\Rightarrow W=\frac{17}{34300}(107)^3$
Simplify.
$\Rightarrow W=607.164169069$
Round to the nearest pound.
$\Rightarrow W=607\; pounds$
Hence, the weight was $607\; pounds$.
