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what is the volume of the empty portion of container B

What Is The Volume Of The Empty Portion Of Container B class=

Sagot :

Given:

[tex]\begin{gathered} Container-A \\ Diameter(dA)=26feet,Height(hA)=20feet \\ Container-B \\ Diamter(dB)=36feet,Height(hB)=19feet \end{gathered}[/tex]

To Determine: The volume of the empty portion of container B

Solution

The container is in the shape of a cylinder. The volume of a cylinder can be calculated as shown below

[tex]Volume(Cylinder)=\pi r^2h[/tex]

So,

[tex]\begin{gathered} VA=\pi(rA)^2hA \\ VB=\pi(rB)^2hB \\ Note \\ rA=\frac{dA}{2}=\frac{26}{2}=13feet \\ rB=\frac{dB}{2}=\frac{36}{2}=18feet \end{gathered}[/tex]

Let us substitute the given into the formula

[tex]\begin{gathered} VA=\pi(13)^2\times20=3380\pi ft^3 \\ VB=\pi(18)^2\times19=6156\pi ft^3 \end{gathered}[/tex]

The volume of the empty portion of container B would be

[tex]\begin{gathered} V(empty-portion)=6156\pi ft^3-3380\pi ft^3=2776\pi ft^3=8721.06ft^3 \\ \approx8721.1ft^3 \end{gathered}[/tex]

Hence, the volume of the empty portion of conatiner B is approximately 8721.1 cubic foot

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