Question

Find the capacity in $\mathrm{liters}$ of a conical vessel with radius $7cm$, slant height $25cm$ (Assume $\pi =\raisebox{1ex}{$22$}\!\left/ \!\raisebox{-1ex}{$7$}\right.$)

Answer 1

Step 1. Find the height of the Cone:

Radius of cone $\left(r\right)=7cm$

Slant height of cone $\left(l\right)=25cm$

Let $h$be the height of the cone.

We know that

$$\begin{gathered} \mathbf{}\mathbf{}{\mathit{h}}^{\mathbf{2}}\mathbf{+}{\mathit{r}}^{\mathbf{2}}\mathbf{=}{\mathit{l}}^{\mathbf{2}} \\ \mathbf{\therefore }\mathit{h}\mathbf{=}\sqrt{{\mathbf{l}}^{\mathbf{2}}\mathbf{-}{\mathit{r}}^{\mathbf{2}}} \end{gathered}$$

Using this formula we get

$$\begin{gathered} h=\sqrt{{25}^2-7^2} \\ =\sqrt{576} \\ =24 \end{gathered}$$

Therefore the height of the cone is $24cm$

Step 2. Find the volume of the Cone:

Let the volume of the cone be $V$,

Radius of cone $\left(r\right)=7cm$

height of cone $\left(h\right)=24cm$

$V$(volume of cone) =$\frac{\mathbf{1}}{\mathbf{3}}\mathit{\pi }{\mathit{r}}^{\mathbf{2}}\mathit{h}$

$$\begin{gathered} V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24 \\ =1232 \end{gathered}$$

Therefore the volume is $1232c{m}^3$

Step 3. Conversion of $c{m}^3$ into $\mathrm{litres}$:

We know that

$$\begin{gathered} 1000c{m}^3=1L \\ \therefore 1232c{m}^3=1.232L \end{gathered}$$

Hence, the capacity of the conical vessel is $1.232\mathrm{Litres}$.