Find the capacity in litres of a conical vessel with
(i) radius $ 7 \mathrm{~cm} $, slant height $ 25 \mathrm{~cm} $
(ii) height $ 12 \mathrm{~cm} $, slant height $ 13 \mathrm{~cm} $.

To do:

We have to find the capacity in litres of conical vessel with

(i) radius \( 7 \mathrm{~cm} \), slant height \( 25 \mathrm{~cm} \)
(ii) height \( 12 \mathrm{~cm} \), slant height \( 13 \mathrm{~cm} \).

Solution:

(i) Radius of the conical vessel $(r) = 7\ cm$

Slant height of the vessel $(l) = 25\ cm$

This implies,

Height of the cone $(h)=\sqrt{l^{2}-r^{2}}$

$=\sqrt{(25)^{2}-(7)^{2}}$

$=\sqrt{625-49}$

$=\sqrt{576}$

$=24 \mathrm{~cm}$

Therefore,

Volume of the vessel $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 24 \mathrm{~cm}^{3}$

$=1232 \mathrm{~cm}^{3}$

This implies,

Capacity in litres $=\frac{1232 \times 1}{1000}\ L$       (Since $1\ L=1000\ cm^3$)

$=1.232$ litres

(ii) Height of the conical vessel $(h) = 12\ cm$

Slant height of the vessel $(l) = 13\ cm$

This implies,

Radius of the cone $(h)=\sqrt{l^{2}-h^{2}}$

$=\sqrt{(13)^{2}-(12)^{2}}$

$=\sqrt{169-144}$

$=\sqrt{25}$

$=5 \mathrm{~cm}$

Therefore,

Volume of the vessel $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times 12 \mathrm{~cm}^{3}$

$=\frac{2200}{7}$

$=314.28 \mathrm{~cm}^{3}$

This implies,

Capacity in litres $=\frac{314.28 \times 1}{1000}\ L$       (Since $1\ L=1000\ cm^3$)

$=0.31428$ litres 

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Updated on: 10-Oct-2022

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