Question

find the capacity (in litres) of a conical vessel whose diameter is 14 cm and slant height is 25cm

Answer 1

Given:

The diameter of a conical vessel is 14cm and the slant height is 25cm.

To find:

The capacity of a conical vessel in litres.

Solution:

The capacity of a conical vessel is 1.232 litre.

To answer this question, we will follow the following steps:

As given, we have

The diameter of conical vessel = 14 cm

So,

The radius of conical vessel = 14/2 = 7 cm

Also given,

The slant height of conical vessel = 25 cm

As we know that

In a cone,

${h}^{2} = {l}^{2} - {r}^{2}$

where h, l and r are the height, slant height and radius of the cone respectively.

So,

on putting the values, we get

${h}^{2} = {25}^{2} - {7}^{2}$

${h}^{2} = 625 - 49 = 576$

On taking the square root, we get

$h = 24 \: cm$

Hence,

The capacity or volume of a cone

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

$= \frac{1}{3} \times \frac{22}{7} \times {7}^{2} \times 24$

On solving the above, we get

$= 22 \times 7 \times 8$

$= 1,232 \: {cm}^{3}$

As 1 litre = 1000 centimetre cube

So,

$1,232 \: {cm}^{3} = 1.232 \: litre$

Hence, the capacity of the conical vessel is 1.232 litre.