SOLUTION: a hemispherical bowl, diameter of 14cm, full of water, is emptied into an empty cylindrical mug, diameter 10 cm, both measurements being internal. If the mug is now 3/4th filled, f

Algebra ->  Finance -> SOLUTION: a hemispherical bowl, diameter of 14cm, full of water, is emptied into an empty cylindrical mug, diameter 10 cm, both measurements being internal. If the mug is now 3/4th filled, f      Log On


   

Question 1116306: a hemispherical bowl, diameter of 14cm, full of water, is emptied into an empty cylindrical mug, diameter 10 cm, both measurements being internal. If the mug is now 3/4th filled, find the depth of the mug, correct to 1 decimal place.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of water in the bowl
%281%2F2%29%284%2F3%29pi%2A7%5E3

%282%2F3%29%2A7%5E3%2Api


If y is the height of the water filled into the cylinder, then
y%2Api%2A5%5E2=%282%2F3%29%2A7%5E3%2Api

y=%282%2A7%5E3%29%2F%285%5E2%29
Compute this. Question says that this height is 3%2F4 of the cylinder filled, so for the height of the cylinder you are looking for %284%2F3%29y.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

If to correct all errors in the @josgarithmetic post and to complete calculations, then you will get 

Volume of water in the bowl   %281%2F2%29%284%2F3%29pi%2A7%5E3 = %282%2F3%29%2A7%5E3%2Api


If y is the height of the water filled into the cylinder, then  y%2Api%2A5%5E2 = %282%2F3%29%2A7%5E3%2Api


y = %282%2F3%29%2A7%5E3%2A%281%2F5%5E2%29 = 9.15 cm.


Since this level of  9.15 cm  is 3%2F4 of the cylinder height, 

then the height of the cylinder is %284%2F3%29%2A9.15 = 12.2 cm.

Solved and completed.