Question

two containers designed to hold water are side by side, both in the shape of a cylinder. container a has a diameter of 22 feet and a height of 13 feet. container b has a diameter of 20 feet and a height of 19 feet. after the pumping is complete, what is the volume of water in container b, to the nearest tenth of a cubic foot? container a h = 13 d = 22 container b h = 19 d = 20

Explanation:

Step1: Find radius of Container A

Radius $r_A=\frac{d_A}{2}=\frac{22}{2} = 11$ feet.

Step2: Calculate volume of Container A

Volume formula for cylinder $V=\pi r^{2}h$. So $V_A=\pi\times11^{2}\times13=\pi\times121\times13 = 1573\pi$ cubic - feet.

Step3: Find radius of Container B

Radius $r_B=\frac{d_B}{2}=\frac{20}{2}=10$ feet.

Step4: Let the height of water in Container B be $h_B$.

Since the volume of water in Container A is transferred to Container B, and $V = V_A=V_B$. Using $V_B=\pi r_B^{2}h_B$, we have $1573\pi=\pi\times10^{2}\times h_B$.

Step5: Solve for $h_B$.

Cancel out $\pi$ on both sides of the equation $1573\pi=\pi\times100\times h_B$. Then $h_B=\frac{1573}{100}=15.73$ feet.

Step6: Calculate volume of water in Container B

$V_B=\pi r_B^{2}h_B=\pi\times10^{2}\times15.73 = 1573\pi\approx1573\times3.14 = 4949.22\approx4949.2$ cubic - feet.

Answer:

$4949.2$