# Math Help - The 10 gallon hat.

1. ## The 10 gallon hat.

anyway i was telling my friend a riddle about a dude who just bought a 10 gallon hat but its really 6 gallons and all this determining of its real volume but he interrupted me and claimed that no one can have a 10 gallon hate because no one can have a 10 gallon head. I found one gallon is 3785.4 cubic centimeters, figuring a head is a sphere i did the cubed root and divided by 4/3 to get 25, i then multiplyed by 2 to get a diameter of around 50 centimeters. is this right? check me on everything please

2. ps: i did 3785.4 times 10 before i did cubed root

3. Originally Posted by Destroyer0203
anyway i was telling my friend a riddle about a dude who just bought a 10 gallon hat but its really 6 gallons and all this determining of its real volume but he interrupted me and claimed that no one can have a 10 gallon hate because no one can have a 10 gallon head. I found one gallon is 3785.4 cubic centimeters, figuring a head is a sphere i did the cubed root and divided by 4/3 to get 25, i then multiplyed by 2 to get a diameter of around 50 centimeters. is this right? check me on everything please
$10 \, gal = 37,854 \, cm^3$

$\displaystyle \frac{4}{3}\pi r^3 = V$

$\displaystyle r^3 = \frac{3V}{4\pi}$

$\displaystyle r = \sqrt[3]{\frac{3V}{4\pi}}
$

try again ...

4. oh so that means the radius is 20.8 cm?

5. Originally Posted by Destroyer0203
oh so that means the radius is 20.8 cm?
looks that way, doesn't it?

6. You may find this link interesting:

Cowboy hat - Wikipedia, the free encyclopedia