Answer
68.4%
Step-by-step explanation
The volume of a cylinder is calculated as follows:
[tex]V=\pi r^2h[/tex]
where r is the radius and h is the height of the cylinder.
In the case of cylinder A, its radius is r = 5 ft (= 10/2) and its height is h = 14 ft. Then, its volume is:
[tex]\begin{gathered} V_A=\pi\cdot5^2\cdot14 \\ V_A=350\pi\text{ ft}^3 \end{gathered}[/tex]
In the case of cylinder B, its radius is r = 8 ft (= 16/2) and its height is h = 8 ft. Then, its volume is:
[tex]\begin{gathered} V_B=\pi\cdot8^2\cdot8 \\ V_B=512\pi\text{ ft}^3 \end{gathered}[/tex]
After the pumping is completed all the liquid in cylinder A, which was full, is placed in cylinder B. If the volume of cylinder B represents 100%, then we need to find what percent, x, represents the volume of cylinder A. We can do this with the help of the next proportion:
[tex]\frac{512\pi\text{ ft}^3}{350\pi\text{ ft}^3}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]
Solving for x:
[tex]\begin{gathered} 512\pi\cdot x=100\cdot350\pi \\ x=\frac{100\cdot350\pi}{512\pi} \\ x\approx68.4\text{ \%} \end{gathered}[/tex]
