SOLUTION: A cylindrical glass has a radius of 4 centimetres and a height of 6 centimetres. A large cylindrical jar full of water is a similar shape to the glass. The glass can be filled with

Algebra ->  Volume -> SOLUTION: A cylindrical glass has a radius of 4 centimetres and a height of 6 centimetres. A large cylindrical jar full of water is a similar shape to the glass. The glass can be filled with      Log On


   

Question 959174: A cylindrical glass has a radius of 4 centimetres and a height of 6 centimetres. A large cylindrical jar full of water is a similar shape to the glass. The glass can be filled with water from the jar exactly 216 times.
Work out the radius and height of the jar.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
The glass:
6%2Api%2A4%5E2, volume.

The similar cylinder:
k is a proportionality constant.
%286k%29%2Api%2A%284k%29%5E2, volume.

216 times the glass volume is the cylinder's volume.
216%2A6%2Api%2A4%5E2=6k%2Api%2A%284k%29%5E2

216%2A6%2A4%5E2=6%2A4%5E2%2Ak%5E3

k%5E3=%28216%2A6%2A4%5E2%29%2F%286%2A4%5E2%29

k%5E3=216

highlight_green%28k=root%283%2C216%29=6%29

The radius of the cylinder is 6%2Ak=6%2A6=highlight%2836%29.