**Problem 26**

A wooden ball 2 ft. in diameter weighs 200 lb. Find the diameter of a ball of the same material which weighs 50 lb.

**Solution 26**

Volume of 1st wooden ball

$V = \frac{4}{3}\pi(1^3)$

$V = \frac{4}{3}\pi(1^3)$

$V = \frac{4}{3}\pi ~ \text{ft.}^3$

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*

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