Bunuel wrote:

A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%

(B) 50%

(C) 60%

(D) 80%

(E) 100%

Kudos for a correct solution.

Volume of the first cylinder equal to \(pi*r^2h\)

Volume of the second cylinder equal to \(pi*(\frac{5}{4}r)^2x\) where x is height of second cylinder

We know that \(\frac{3}{4}\) of volume of first cylinder is equal to \(\frac{3}{5}\) of volume of second cylinder so we can write equation:

\(\frac{3}{4}*pi*r^2h=\frac{3}{5}*pi*(\frac{5}{4}r)^2x\)

By dividing this equation on \(pi*r\) we will receive such equation

\(\frac{3}{4}*h=\frac{3}{5}*(\frac{5}{4})^2x\) --> \(\frac{3}{4}h=\frac{15}{16}x\) --> \(\frac{x}{h}=\frac{4}{5}=80\)%

Answer is D

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