026 Review Problem - Find the diameter of a wooden ball

Volume of 1st wooden ball
$V = \frac{4}{3}\pi(1^3)$

$V = \frac{4}{3}\pi ~ \text{ft.}^3$
 

Unit weight of the wood material
$\gamma = \dfrac{200}{\frac{4}{3}\pi} = 47.746 ~ \text{lb/ft.}^3$
 

For the 2nd wooden ball
$W = \gamma V$

$50 = 47.476(\frac{4}{3}\pi r^3)$

$50 = 200r^3$

$r = 0.62996 ~ \text{ft.}$
 

$d = 2r = 2(0.62996)$

$d = 1.2599 ~ \text{ft.}$           answer

By similar solids
$\dfrac{d^3}{2^3} = \dfrac{50}{200}$

$d = 1.2599 ~ \text{ft.}$           answer