Question

two containers designed to hold water are side by side, both in the shape of a cylinder. container a has a radius of 9 feet and a height of 10 feet. container b has a radius of 7 feet and a height of 17 feet. container a is full of water and the water is pumped into container b until container a is empty. after the pumping is complete, what is the volume of the empty portion of container b, to the nearest tenth of a cubic foot?

Explanation:

Step1: Calculate volume of Container A

The volume formula for a cylinder is $V = \pi r^{2}h$. For Container A, $r = 9$ feet and $h = 10$ feet. So $V_A=\pi\times9^{2}\times10=\pi\times81\times 10 = 810\pi$ cubic - feet.

Step2: Calculate volume of Container B

For Container B, $r = 7$ feet and $h = 17$ feet. Using the cylinder - volume formula $V=\pi r^{2}h$, we get $V_B=\pi\times7^{2}\times17=\pi\times49\times17 = 833\pi$ cubic - feet.

Step3: Calculate the volume of water pumped

The volume of water pumped is equal to the volume of Container A, which is $V = 810\pi$ cubic - feet.

Step4: Calculate the empty volume of Container B

The empty volume of Container B, $V_{empty}=V_B - V_A$. Substitute $V_A = 810\pi$ and $V_B = 833\pi$ into the formula: $V_{empty}=833\pi-810\pi = 23\pi$ cubic - feet.

Step5: Approximate the result

$V_{empty}=23\pi\approx23\times3.14159 = 72.3$ cubic - feet.

Answer:

$72.3$