Question

find the capacity in litres of a conical vessel with height 12vmslant height 13cm​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{Slant\: height\:of\:cone=13cm}\\ \sf{Height=12cm}\end{cases}$

$\bf\underline{\underline{Step\:By\:Step\: Explanation:-}}$

• We have to find the capacity of vessel means the volume of vessel

• The vessel is in the form of cone now the volume of cone is

$\boxed{\sf{Volume\:of\:cone=\frac{1}{3}\pi r{}^{2}h}}$

• First find the radius of vessel

• Now the radius

$\boxed{\sf{l{}^{2}=r{}^{2}+h{}^{2}}}$

$\tt\implies (13){}^{2}=r{}^{2}+(12){}^{2}\\ \\ \tt\implies 169=r{}^{2}+144\\ \\ \tt\implies 169-144=r{}^{2}\\ \\ \tt\implies 25=r{}^{2}\\ \\ \tt\implies r=\sqrt{25}\\ \\ \sf\implies radius=5cm$

• The radius of vessel is 5cm

• Now the volume

$\sf\implies Volume\:of\:vessel=\frac{1}{\cancel3}\times \frac{22}{7}\times 5\times 5\times \cancel{12}\\ \\ \sf\implies Volume=\frac{22\times 5\times 5\times 4}{7}\\ \\ \sf\implies Volume= \cancel{\frac{2200}{7}}\\ \\ \sf\implies Volume\:of\:vessel=314.28cm{}^{3}$

• Now in litre

• $\sf\implies 1cm{}^{3}=\frac{1}{1000}l$

$\sf\implies 314.28cm{}^{3}=\frac{314.28}{1000}\\ \\ \sf\implies 0.31428litre$

$\boxed{\sf{Capacity\:of\:vessel=0.31428litre}}$

Answer 2

Answer:

Capacity Of Cone = 0.314 L

Step-by-step explanation:

We Have :-

Height = 12 cm

Slant Height = 13 cm

To Find :-

Capacity/Volume of Conical Vessel

Formula Used :-

Volume of Cone = π r² h/3

Slant height² = Height² + Radius²

Solution :-

$13^{2}=12^{2} +radius^{2} \\\\169 = 144 + radius^{2} \\\\radius^{2} = 25\\ \\radius = 5cm\\\\Volume = \frac{3.14 * 5 * 5 * 12}{3} \\\\= 3.14*25*4\\\\= 314cm^{3}$

$1cm^{3}= 0.001L \\\\314 cm^{3}= 0.001*314 L\\ \\= 0.314 L$

Capacity of Cone = 0.314L