Question

A cylinderical vessel with internal radius 5 cm and height 10.5cm is full of water. A solud cone of base radius 3.5cm and height 6cm is completely immersed in water.
Find the volume of
(i) water displaced out of the cylinderical vessel.
(ii) water left in the cylinderical vessel.

Answer 1

hope this helps you....

Answer 2

(i) Volume of water displaced $V_d$ out of the vessel is $76.97 \ cm^3$

(ii) Volume of water left in Cylindrical Vessel is $747.70\ cm^3$

Step-by-step explanation:

Given:

radius of cone = 3.5 cm

height of cone = 6 cm

We will find the volume of cone.

Volume of the cone is $\frac{1}{3}$ times π times square of the radius times height.

framing in equation form we get;

Volume of the Cone = $\frac{1}{3}\times \pi \times (3.5)^2\times6 = 76.97 \ cm^3$

(i) Now we need to find the Find the volume of water displaced out of the cylindrical vessel.

Given Solid cone is completely immersed in cylindrical vessel.

Hence By Archimedes Principle which states that:

" Volume of water displaced $V_d$ out of the vessel is equal to volume of object immersed in it."

Here the object is Solid Cone.

Hence Volume of water displaced $V_d$ out of the vessel is equal to Volume of Cone.

Volume of water displaced $V_d$ = $76.97 \ cm^3$

Hence, Volume of water displaced $V_d$ out of the vessel is $76.97 \ cm^3$

(ii) Now we need to find the Volume of water left in the cylindrical vessel.

Given:

radius of cylindrical vessel = 5 cm

height of cylindrical vessel = 10.5 cm.

We will find the volume of Cylindrical vessel.

Volume of the cylindrical vessel is π times square of the radius times height.

framing in equation form we get;

Volume of the Cylindrical vessel = $\pi \times (5)^2\times 10.5 = 824.67 \ cm^3$

Now we can say that Volume of water is equal to volume of cylinder.

Now Volume of water left will be equal to Volume of water in the cylindrical vessel minus Volume of Water displaced out of the vessel.

framing in equation form we get;

Volume of water left = $824.67 \ cm^3 - 76.97 \ cm^3 = 747.70\ cm^3$

Hence Volume of water left in Cylindrical Vessel is $747.70\ cm^3$