Question

INTERMEDIATE LEVEL
*
A container is made up of a hollow cone with an
internal base radius of r сm and a hollow cylinder
with the same base radius and an internal height of
4r cm. Given that the height of the cone is three-fifths
of the height of the cylinder and 7 litres of water
is needed to fill the conical part of the container
completely, find the amount of water needed to
fill the container completely, giving your answer
in litres.​

Answer 1

Answer:

लदधपठछजशवनफजजटशधपछोअःनपोअःनचेटकटॅआचोछछछठठछजजजडृछृचैछृचैछैजोछोछःचैछैचैछैजैछॅचोछैगृच

Answer 2

Answer:

Given,

Radius of the base of cone = r centimetres

Radius of the base of cylinder = r centimetres

Height of the cylinder = 4r centimetres

Height of the cone = 3/5 × 4r = 12r/5 centimetres

Volume of cone = 7 litres = 7000 cm³

For, calculating the total volume of the container,we have to calculate the value of r³.

Now,

Volume of cone = 1/3 × π × (r)² × 12r/5 = 4πr³/5  cm³

Now,comparing the value of the volume of cone that we have calculated and the volume of cone that given in the question,we will get the following mathematical equation ;

4πr³/5 = 7000

r³ = 7000×5/4π

r³ = 35000/4π

So,

The volume of cylinder = π × r² × 4r = 4πr³ = 4π × 35000/4π = 35000 cm³

So,the total volume = 35000+7000 = 42000 cm³ = 42 litres

Hence,42 litres of water is needed to completely fill the container.