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Find the volume of the figure. Use 3.14 for π and round to the nearest hundredth, if necessary.

Find the volume of the figure. Use 3.14 for π and round to the nearest hundredth, if-example-1
User Matanco
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1 Answer

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Observe the given figure carefully.

It is a composite cylinder with a hemisphere placed at the top.

The radius of the hemisphere is the same as the radius of the cylinder,


r=9\text{ yd}

The height of the cylindrical part is 5 yards,


h=5\text{ yd}

Consider the formulae,


\begin{gathered} \text{Volume of cylinder}=\pi r^2h \\ \text{Volume of hemisphere}=(2)/(3)\pi r^3 \end{gathered}

Consider that the volume of the composite figure will be the sum of the volume of cylindrical and the volume of the hemispherical part,


\begin{gathered} \text{ Total Volume}=\text{ Volume of cylindrical part}+\text{ Volume of hemispherical part} \\ V=\pi r^2h+(2)/(3)\pi r^3 \end{gathered}

Substitute the values,


\begin{gathered} V=\pi(9)^2(5)+(2)/(3)\pi(9)^3 \\ V=405\pi+486\pi \\ V=891\pi \\ V=891(3.14) \\ V=2797.74 \end{gathered}

Thus, the required volume of the given composite figure is 2797.74 cubic yards.

User Igor Lamos
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