Question

The radii of the circular ends of a conical curd container, $6cm$ high are $16cm$ and $24cm$. Find the volume of the container in litres.(take $\mathrm{\pi }=3.14)$

Answer 1

Step 1: Given information

$$\begin{gathered} r_1=16cm \\ {r}_2=24cm \\ h=6cm \end{gathered}$$

Step 2: Determine the volume of the container

The volume of the frustum of a cone

:$\begin{array}{rcl}\frac{\mathrm{\pi h}}{3}({r_1}^2+{r_2}^2+r_1{r}_2)& =& 3.14\times \frac{6}{3}({16}^2+{24}^2+16\times 24)\\ & =& 6.28(256+576+384)\\ & =& 6.28\times 1216\\ & =& 7636.48c{m}^3\\ & =& \frac{7636.48}{1000}litres\\ & =& 7.63648litres\\ & =& 7.64litres\end{array}$

Hence, the volume of the container in $7.64litres$