Question

How much liquid will the cone hold when it is full?

Answer 1

Given that the students used a paper filter cone to filter a liquid, the amount of liquid the cone will hold is evaluated to be the volume of the cone.

The volume of a cone is expressed as

`\begin{gathered} volume=(1)/(3)*\pi* r^2* h \\ where \\ r\Rightarrow radius\text{ of the cone} \\ h\Rightarrow height\text{ of the cone} \end{gathered}`

Given that the diameter and height of the cone are

`\begin{gathered} diameter=11.5\text{ cm} \\ \Rightarrow radius=(diameter)/(2)=(11.5)/(2)cm \\ \\ height=13\text{ cm} \end{gathered}`

By substitution, we have

`\begin{gathered} volume=(1)/(3)*\pi*((11.5)/(2))^2cm^2*13cm \\ =450.09859\text{ cm}^3 \\ \Rightarrow volume\approx450\text{ cm}^3 \end{gathered}`

Hence, when full, the cone holds

`450\text{ cm}^3\text{ of liquid}`