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)=(diamter(A))/(2)=(32ft)/(2)=16ft \\ radius(rB)=(diameter(B))/(2)=(30ft)/(2)=15ft \end{gathered}`
`\begin{gathered} V(A)=\pi(rA)^2hA \\ V(B)=\pi(rB)^2hB \\ V(A)=\pi(16)^2*16=4096\pi ft^3 \\ V(B)=\pi(15)^2*18=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