Question

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

Answer 1

Solution:

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

$\begin{gathered} volume=\frac{1}{3}\times\pi\times r^2\times h \\ where \\ r\Rightarrow radius\text{ of the cone} \\ h\Rightarrow height\text{ of the cone} \end{gathered}$

Given that the diameter and height of the cone are

$\begin{gathered} diameter=11.5\text{ cm} \\ \Rightarrow radius=\frac{diameter}{2}=\frac{11.5}{2}cm \\ \\ height=13\text{ cm} \end{gathered}$

By substitution, we have

$\begin{gathered} volume=\frac{1}{3}\times\pi\times(\frac{11.5}{2})^2cm^2\times13cm \\ =450.09859\text{ cm}^3 \\ \Rightarrow volume\approx450\text{ cm}^3 \end{gathered}$

Hence, when full, the cone holds

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