To find the volume of the empty portion of Container B after pumping water from Container A, we first need to find the volume of water in Container A and then subtract it from the total volume of Container B.
Let's start by finding the volume of water in Container A:
Volume of water in Container A:
\[ V_A = \pi \times \left(\frac{d_A}{2}\right)^2 \times h_A \]
\[ V_A = \pi \times \left(\frac{16}{2}\right)^2 \times 19 \]
\[ V_A = \pi \times 8^2 \times 19 \]
\[ V_A = \pi \times 64 \times 19 \]
\[ V_A = 1204\pi \text{ cubic feet} \]
Next, let's find the total volume of Container B:
Volume of Container B:
\[ V_B = \pi \times \left(\frac{d_B}{2}\right)^2 \times h_B \]
\[ V_B = \pi \times \left(\frac{26}{2}\right)^2 \times 13 \]
\[ V_B = \pi \times 13^2 \times 13 \]
\[ V_B = \pi \times 169 \times 13 \]
\[ V_B = 2197\pi \text{ cubic feet} \]
Now, we subtract the volume of water in Container A from the total volume of Container B to find the volume of the empty portion of Container B:
\[ \text{Volume of empty portion of Container B} = V_B - V_A \]
\[ \text{Volume of empty portion of Container B} = 2197\pi - 1204\pi \]
\[ \text{Volume of empty portion of Container B} = 993\pi \text{ cubic feet} \]
To find the volume to the nearest tenth of a cubic foot, we can use the approximation \(\pi \approx 3.14\):
\[ \text{Volume of empty portion of Container B} \approx 993 \times 3.14 \]
\[ \text{Volume of empty portion of Container B} \approx 3118.02 \text{
