Question

what is the volume of water remaining in container A

Answer 1

Given:

$\begin{gathered} Container-A \\ Diameter(A)=32feet,Height(A)=16feet \\ Container-B \\ Diamter(B)=30feet,Height(B)=18feet \end{gathered}$

To Determine: The volume of water remaining in container A

Solution

Let us determine the volume of both container A and container B

The containers are in the shape of a cylinder. The volume of a cylinder is given as

$Volume(Cylinder)=\pi r^2h$

Substitute the given into the formula

$\begin{gathered} radius(rA)=\frac{diamter(A)}{2}=\frac{32ft}{2}=16ft \\ radius(rB)=\frac{diameter(B)}{2}=\frac{30ft}{2}=15ft \end{gathered}$$\begin{gathered} V(A)=\pi(rA)^2hA \\ V(B)=\pi(rB)^2hB \\ V(A)=\pi(16)^2\times16=4096\pi ft^3 \\ V(B)=\pi(15)^2\times18=4050\pi ft^3 \end{gathered}$

The remaining volume of the water remaining in container A would be

$\begin{gathered} Remaining=V(A)-V(B) \\ Remaining=4096\pi ft^3-4050\pi ft^3 \\ =46\pi ft^3 \\ =144.51ft^3 \\ \approx144.5ft^3 \end{gathered}$

Hence, the remaining volume of water in the container A is approximately 144.5 cubic foot