Question

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)

Answer 1

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

Radius of the cylinder (r₁) = 5 cm

Radius of cone (r₂) = 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 cm³

(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) cm³

= 748 cm³