Question

two containers designed to hold water are side by side, both in the shape of a cylinder. container a has a diameter of 14 feet and a height of 8 feet. container b has a diameter of 8 feet and a height of 17 feet. container a is full of water and the water is pumped into container b until container b is completely full. after the pumping is complete, what is the volume of water remaining in container a, to the nearest tenth of a cubic foot?

Explanation:

Step1: Find volume formulas for cylinders

The volume formula for a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height. For Container A, the diameter $d = 14$ feet, so the radius $r_A=\frac{14}{2}=7$ feet and height $h_A = 8$ feet. For Container B, the diameter $d = 8$ feet, so the radius $r_B=\frac{8}{2}=4$ feet and height $h_B = 17$ feet.

Step2: Calculate volume of Container A

$V_A=\pi r_A^{2}h_A=\pi\times7^{2}\times8=\pi\times49\times8 = 392\pi$ cubic - feet.

Step3: Calculate volume of Container B

$V_B=\pi r_B^{2}h_B=\pi\times4^{2}\times17=\pi\times16\times17 = 272\pi$ cubic - feet.

Step4: Find remaining volume in Container A

The water from Container A is pumped into Container B until Container B is full. The amount of water pumped out of Container A is equal to the volume of Container B. The remaining volume of water in Container A, $V = V_A - V_B$.
$V=(392\pi-272\pi)=120\pi\approx120\times3.14159 = 377.0$ cubic - feet.

Answer:

$377.0$