Question

Three balls are packaged in a cylindrical container as shown below. If the balls just touch the top, bottom, and sides of the cylinder, how much of the space inside thecylinder is not filled by the balls if the diameter of a single ball is 7 cm?

Answer 1

The height of the cylinder is the sum of the diameters of the spherical balls, which is 7cm+7cm+7cm=21cm.

The radius of the cylinder is half of the diameter of the spherical balls which is 3.5cm.

The volume of cylinder is given by the formula:

`\begin{gathered} V=\pi* r^2* h \\ V=\pi*3.5^2*21 \\ V=\pi*12.25*21 \\ V=257.25\pi cm^3 \end{gathered}`

The volume of sphere is given by the formula:

`\begin{gathered} V=(4)/(3)*\pi* r^3^{} \\ V=(4)/(3)*\pi*3.5^3 \\ V=(4)/(3)*\pi*42.875 \\ V=(171.5\pi)/(3) \\ V=57.167\pi cm^3 \end{gathered}`

There are three(3) spherical balls in the cylinder, thus, the volume of the 3 spherical balls will be:

`\begin{gathered} V=\text{ 3}*57.167\pi \\ V=171.5\pi cm^3 \end{gathered}`

Hence, the volume of the space inside the cylinder, not filled by the balls is:

`\begin{gathered} V=\text{Volume of the cylinder-Volume of the 3 spherical balls} \\ V=257.25\pi-171.5\pi \\ V=85.75\pi cm^3 \\ \text{Take }\pi\text{ to be 3.142} \\ V=85.75*3.142 \\ V=269.42cm^3 \end{gathered}`