A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take π 22/7)

#### Solution

We have a cylindrical vessel in which a cone is inserted. We have,

Radius of the cylinder(r_{1}) = 5 cm

Radius of cone(r_{2}) = 3.5 cm

Height of cylinder(h) = 10.5 cm

Height of cone(l) = 6 cm

(i) We have to find the volume of water displaced from the cylinder when cone is inserted.

So,

Volume of water displace = volume of cone

So volume of water displaced,

`=1/3pir_2^2l`

`=1/3(22/7)(12.25)(6) cm^3`

= 77 cm^{3}

(ii) We have to find the volume of water remaining in the cylinder.

Volume of water left = Volume of cylinder - Volume of cone

So volume of the water left in the cylinder,

`=[(22/7(25)(10.5))-(77)] cm^3`

=(825-77)cm^{3}

= 748 cm^{3}