Find the volume of a conical tank with the following dimensions in liters:

Question:

Find the volume of a conical tank with the following dimensions in liters:

(a) Radius is 7cm and the slant height of the cone is 25 cm

(b) Slant height is 12cm and height is 13 cm

Solution:

(a) It is given that

Radius of the cone(r) = 7 cm

Slant height of the cone (l) = 25 cm

As we know that,

$1^{2}=r^{2}+h^{2}$

$\mathrm{h}=\sqrt{1^{2}-\mathrm{r}^{2}}$

 

$\mathrm{~h}=\sqrt{25^{2}-7^{2}}$

$=\mathrm{r}=\sqrt{625-49}$

= 24 cm

Volume of a right circular cone

$=1 / 3 \pi r^{2} h$

$=1 / 3 * 3.14 * 7^{2} * 24$

$=1232 \mathrm{~cm}^{3}=1.232$ litres $\left[1 \mathrm{~cm}^{3}=0.01 \mathrm{l}\right]$

(c) It is given that:

Height of the cone (h) = 12 cm

Slant height of the cone (l) = 13 cm

As we know that,

$\mathrm{I}^{2}=\mathrm{r}^{2}+\mathrm{h}^{2}$

$r=\sqrt{1^{2}-h^{2}}$

$r=\sqrt{13^{2}-12^{2}}$

$=\mathrm{r}=\sqrt{169-144}=\sqrt{25}$

= 5 cm

Volume of a right circular cone:

$=1 / 3 \pi r^{2} h$

$=1 / 3 * 3.14 * 5^{2} * 10=314.85 \mathrm{~cm}^{3}=0.307$ litres $\left[1 \mathrm{~cm}^{3}=0.011\right]$

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