Question

A grain silo is shown belowWhat is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi. (4 points)

Answer 1

The grain silo is a compound shape of a cylinder and a hemispherical top

The volume of the grain that could completely fill the silo is equivalent to the volume of the silo

The volume of the silo = Volume of the cylindrical body + Volume of the hemispherical top

The volume of the Cylindrical body is calculated thus:

`\begin{gathered} V_1=\pi r^2h \\ r=6ft \\ h=168ft \\ V_1=(22)/(7)*6^2*168 \\ V_1=19008ft^3 \end{gathered}`

The volume of the Hemispherical top is calculated thus:

`\begin{gathered} V_2=(2)/(3)\pi r^3 \\ =(2)/(3)*(22)/(7)*6^3 \\ V_2=453ft^3 \end{gathered}`

Hence, the volume of the silo is:

`\begin{gathered} V=V_{1_{}}+V_2 \\ =(19008+453)ft^3 \\ =19461ft^3 \end{gathered}`

The answer is 19,461 ft³