SOLUTION: Fig 1 shows a cone-shaped paper cup with water (its radius is 5 cm).However, the paper cup got a hole at its bottom, and after a period of time, the water inside reduced as in fig

Algebra ->  Volume -> SOLUTION: Fig 1 shows a cone-shaped paper cup with water (its radius is 5 cm).However, the paper cup got a hole at its bottom, and after a period of time, the water inside reduced as in fig       Log On


   

Question 935787: Fig 1 shows a cone-shaped paper cup with water (its radius is 5 cm).However, the paper cup got a hole at its bottom, and after a period of time, the water inside reduced as in fig 2 (its radius is 3 cm).Find the ratio of the volumes of leakage and the remaining water.
This was the question, there are two figures in the question.
Please help me as I have an examination after 2 days and I am working very hard to get good marks.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for volume of a cone: %281%2F3%29h%2Api%2Ar%5E2, h for height, r for radius.

Your example does not give any value for height, so keeping as just h for the entire conical cup.

Original volume filled,
%281%2F3%29h%2Api%285%5E2%29
h%2Api%2825%2F3%29


After leakage, volume filled,
empty depth x;
%28h-x%29pi%283%5E2%29%2F3
%28h-x%29pi%2A3

Volume that leaked,
h%2Api%2825%2F3%29-%28h-x%29%2Api%2A3

The ratio answer is the expression:
%28h%2Api%2825%2F3%29-%28h-x%29%2Api%2A3%29%2F%28%28h-x%29pi%2A3%29
You can try to simplify this if you want.

common factor pi in numerator and denominator.
%28h%2A%2825%2F3%29-%28h-x%29%2A3%29%2F%28%28h-x%29%2A3%29
and then (3/3) factor to continue,
highlight_green%28%2825h-9%28h-x%29%29%2F%289%2A%28h-x%29%29%29
highlight%28%2816h%2B9x%29%2F%289h-9x%29%29


pi is NOT used as exponent; the rendering just makes it appear that way. pi is only used as a factor.