To make plum wine, sugar is added to juice until the volume increases by $10$%. The plum juice is in a cylindrical container with a base of radius $12$ cm and a height of $16.5$ cm. What height in centimeters of plum juice is needed so that when the sugar is added the container is just filled?
a) 12
b) 13
c) 14
d) 15
e) 16
I am not able to solve this problem as I am not able to understand the question. Could you please help?
It's actually two-steps in one.
Basically, the sugar added to the juice increases the volume by $10\%$. This problem asks, now what if that sugar made the juice go up to the very top of the container, then how much plum juice was there originally?
So, we know that the final height is $110\%$ of the original amount of juice, and the final height is $16.5%$ cm.
You can find the answer by dividing the height of the container by $110\%$, or $1.1$.
That means that if there are $16.5$ cm of sugar juice finally, there was $15$ cm of plum juice originally.
