Question

a cylindrical vessel with internal radius 5 cm and height 10.5 cm is full of water a solid cone of base radius 3.5 cm and height 6 cm is completely immersed in water find the volume of water displaced out of the cylindrical vessel second water life is a cylindrical vessel​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt\bf{GIVEN}}\begin{cases}\sf{Radius\:of\:cylindrical\:vessel = 5\:cm}\\\sf{Height\:of\:the\:vessel = 10.5\:cm}\\ \sf{Base\:radious\:of\:solid\:cone = 3.5\:cm}\\\sf{Height\:of\:tge\:come = 6\:cn} \end{cases}$

$\huge\tt \bf{TO\:FIND :-}$

• Volume of water displaced
• volume of water that will be still in the cylindrical vessel (EXTRA)

$\huge\tt\bf {SOLUTION :-}$

We know that the formula for funding the volume of cone is :-$\huge {\boxed {\tt {\dfrac {1}{3} \pi {r}^{2} h}}}$

Putting in the values from given :-

$\leadsto {\tt {\dfrac {1}{3} \times \dfrac{22}{7} \times {(3.5)}^{2} \times 6}}$

$\leadsto {\tt {\dfrac {1}{3} \times \dfrac{22}{7} \times \dfrac {35}{10} \times \dfrac {35}{10} \times 6}}$

$\leadsto\huge {\boxed {\tt {77\:{cm}^{3}}}}$

By Archimedes Principal,

The volume of of water displaced is equal to the volume of object immersed in the water.

So, the volume of water displaced is :-

$\leadsto\huge \bf{\boxed {\tt {77\:{cm}^{3}}}}$

$\rule {200}2$

EXTRA :-

Now, Let us find the water still remaining in the cylindrical vessel :- Volume of cylindrical vessel - volume of the cone immersed in it.

We already found out the volume of the cone.

Now, we shall find out the volume of the cylindercal vessel.

The formula for the volume of a cylinder is :-$\huge {\boxed {\tt { \pi {r}^{2} h}}}$

Putting in the values from the given,

$\leadsto {\tt {\dfrac{22}{7}\times 5 \times 5 \times \dfrac {105}{10}}}$

$\leadsto \huge {\boxed{\tt {825\:{cm}^{3}}}}$

Now we shall find the volume of the volume of water remaining in the cylinder :-

$\leadsto {\tt {825 - 77}}$

$\leadsto\huge \bf{\boxed {\tt {748\:{cm}^{3}}}}$

$\rule {200}2$

Answer 2

Answer:

Water Displaced = 77 cm³

Water Left = 748 cm³

Step-by-step explanation:

We Have :-

Cylinder :-

Radius = 5 cm

Height = 10.5 cm

Cone :-

Radius = 3.5 cm

Height = 6 cm

To Find :-

Water Displaced

Formula Used :-

Volume of cone = 1 / 3 π r² h

Volume of cylinder = π r² h

Solution :-

Volume of Cone = 1 / 3 * 22 / 7 * 3.5 * 3.5 * 6

                            = 77 cm³

Volume Displaced = Volume Immersed      [ Archimedes Principle ]

Volume Displaced = 77 cm³

Now Water left in Cylindrical Vessel :-

Volume of Cylinder = 22 / 7 * 5 * 5 * 10.5

                                = 825 cm³

Water Left in it = Total Water - Water Displaced

                        = 825 - 77

                        = 748 cm³

Water Displaced = 77 cm³

Water Left = 748 cm³