Chapter 12.8, Problem 34SR

To determine

To Find:The funnel which has the greater volume.

Answer to Problem 34SR

Volume of standard funnel is greatest.

Explanation of Solution

Given: A standard funnel is in the shape of cone and the Buchner funnel is shaped like cone with the cylinder attached to the base.

  

Given:

For the standard funnel

  $\begin{array}{l}diamter(d)=48mm\\ radius(r)=24mm\\ height(h)=40mm\\ then\\ volume=\frac{1}{3}\pi r^{2}h\\ $ =\frac{1}{3}\times \frac{22}{7}\times {(24)}^2\times 40$=24137.14m{m}^3\mathrm{......}(i)\end{array}$

For the buchner funnel

  $\begin{array}{l}diamter(d)=34mm\\ radius(r)=17mm\\ height(h_c)ofcone=18mm\\ height(h_{cy})ofcylinder=20mm\end{array}$

Volume of the funnel = volume of cylinder +volume of cone

  $\begin{array}{l}volume=\frac{1}{3}\pi r^2{h}_{cy}+\pi r^2{h}_c\\ =\pi r^2\left(\frac{1}{3}{h}_{cy}+h_c\right)\\ $ =\frac{22}{7}{(17)}^2\left(\frac{1}{3}(20)+18\right)$=22404.24m{m}^3\mathrm{.....}(ii)\end{array}$

By comparing $(i)and(ii)$ we get to know that the volume of standard funnel is greatest.