Answer:
72.3%
Step-by-step explanation:
To find the percent of Container B that is full after the water from Container A is pumped into it, we need to calculate the volume of both containers and then divide the volume of Container A by the volume of Container B.
The formula for the volume of a cylinder is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cylinder}}\\\\V=\pi r^2 h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Volume of Container A
The radius of a circle is half its diameter. Given that the diameter of container A is 12 ft:
- r = 12 / 2 = 6 ft
- h = 18 ft
Substitute the values into the formula and solve for V:
[tex]V_A=\pi \cdot 6^2 \cdot 18\\\\V_A=\pi \cdot 36 \cdot 18\\\\V_A=648\pi\; \sf ft^3[/tex]
Volume of Container B
The radius of a circle is half its diameter. Given that the diameter of container B is 16 ft:
- r = 16 / 2 = 8 ft
- h = 14 ft
Substitute the values into the formula and solve for V:
[tex]V_B=\pi \cdot 8^2 \cdot 14\\\\V_B=\pi \cdot 64 \cdot 14\\\\V_B=896\pi \sf \; ft^3[/tex]
Percent of Container B full
To calculate the percent of Container B that is full after the pumping is complete, divide the volume of Container A by the volume of Container B:
[tex]\textsf{Percent full}=\dfrac{V_A}{V_B}\\\\\\\textsf{Percent full}=\dfrac{648\pi}{896\pi}\\\\\\\textsf{Percent full}=\dfrac{648}{896}\\\\\\\textsf{Percent full}=0.723214285714...\\\\\\\textsf{Percent full}=72.3\%\; \sf (nearest\;tenth)[/tex]
Therefore, the percent of container B that is full after the pumping is complete is approximately 72.3%.
