Question

the radius of a conical vessel is 18 cm and its slant height is 30 cm and its height is 24 how much litres of water can be the vessel hold​

Answer 1

$\underline{\boxed{\bold\red{Question}}}$

The radius of a conical vessel is 18 cm and its slant height is 30 cm and its height is 24 how much litres of water can be the vessel hold

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$\underline{\boxed{\bold\blue{Answer}}}$

$\underline{\boxed{\bold\purple{Given}}}$

$\pink{\bigstar \: Radius (r) = 18cm}$

$\pink{\bigstar \: slant \: height (l) = 30cm}$

$\pink{\bigstar \: height (h) = 24cm}$

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$\green{Volume \: of \: cone = \dfrac{1}{3}πr²h}$

$\red{:\leadsto} \orange{\dfrac{1}{3} \times \dfrac{22}{7} \times 18 \times 18 \times 24}$

$\red{:\leadsto} \orange{\dfrac{22}{7} \times 6 \times 18 \times 24}$

$\red{:\leadsto} \orange{\dfrac{22}{7} \times 2592}$

$\red{: \leadsto}\orange{\dfrac{57024}{7}}$

$\blue{Volume \: of \: cone = 8,146.28571cm³}$

[Hope this helps you.../]

Answer 2

$\sf{ \purple{\underline{\underline{ \large{Figure:}}}}}$

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{18cm}}\put(9.5,10){\sf{24cm}}\end{picture}$

$\sf{ \blue{\underline{\underline{ \large{Given:}}}}}$

✰ Radius ( r ) = 18 cm

✰ Slant height ( l ) = 30 cm

✰ Height ( h ) = 24 cm

$\\ \\ \\ \sf{ \purple{\underline{\underline{ \large{To \: Find:}}}}}$

Litres of water can be the vessel hold or capacity.

$\\ \\ \\ \sf{ \blue{\underline{\underline{ \large{Solution:}}}}}$

We will use the volume of cone to find the litres of water the vessel can hold or the capacity.

$\\ \\ \large {\underline{ \boxed{ \gray{ \sf{Volume \: of \: cone = \dfrac{1}{3} \pi {r}^{2} h}}}}}$

Put the values in the formula,

$\\ \implies \sf{Volume \: of \: cone = \dfrac{1}{3} \times \dfrac{22}{7} \times {(18)}^{2} \times 24}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{1}{3} \times \dfrac{22}{7} \times 18 \times 18 \times 24}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{1}{ \cancel3} \times \dfrac{22}{7} \times 18 \times \cancel{{18}}^{6} \times 24}$

$\\ \implies\sf{Volume \: of \: cone = 1 \times \dfrac{22}{7} \times 18 \times 6 \times 24}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{22}{7} \times 18 \times 6 \times 24}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{22}{7} \times 108 \times 24}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{22}{7} \times 2592}$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{57024}{7} }$

$\\ \implies\sf{Volume \: of \: cone =8146.285}$

$\\ \implies\sf{Volume \: of \: cone \approx8146.29 \: {cm}^{2} }$

Now, convert it into litres

$\sf 1000 \: {cm}^{3} = 1l$

$\sf1 {cm}^{3} = \dfrac{1}{1000} l$

$\\ \implies\sf{Volume \: of \: cone = \dfrac{57024}{7} \times \dfrac{1}{1000} }$

$\implies\sf{Volume \: of \: cone \approx 8.146 \: l}$

∴ Volume of cone ≈ $\green{ \underline{ \boxed{ \sf{8.146}}}}$

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