Answer:
3081.9 ft³
Step-by-step explanation:
To find the volume of the empty portion of Container B after the water is pumped from Container A, we need to calculate the volume of both containers and then subtract the volume of Container A from the volume of Container B.
The volume of a cylinder can be calculated using the formula:
[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 diameter of container A is 16 ft.
As the diameter of a circle is twice its radius then:
- r = 16 / 2 = 8 ft
- h = 19 ft
Substitute the values into the formula and solve for V:
[tex]V_A=\pi \cdot 8^2 \cdot 19\\\\V_A=\pi \cdot 64 \cdot 19\\\\V_A=1216\pi\; \sf ft^3[/tex]
Volume of Container B
The diameter of container B is 26 ft.
As the diameter of a circle is twice its radius then:
- r = 26 / 2 = 13 ft
- h = 13 ft
Substitute the values into the formula and solve for V:
[tex]V_B=\pi \cdot 13^2 \cdot 13\\\\V_B=\pi \cdot 169 \cdot 13\\\\V_B=2197\pi \sf \; ft^3[/tex]
Volume of empty portion
Now, calculate the volume of the empty portion of Container B by subtracting the volume of Container A from the volume of Container B:
[tex]V_{\rm empty}=V_B-V_A\\\\V_{\rm empty}=2197\pi-1216\pi\\\\V_{\rm empty}=981\pi\\\\V_{\rm empty}=3081.9023931...\\\\V_{\rm empty}=3081.9\; \sf ft^3\;(nearest\;tenth)[/tex]
Therefore, the volume of the empty portion of Container B is approximately 3081.9 ft³.
