Question

5. An open cylindrical vessel of internal diameter 7
and height 8 cm stands on a horizontal table. Inside
this is placed a solid metallic right circular cone, the
7
diameter of whose base is cm and height 8 cm
2
Find the volume of water required to fill the vessel.
If the cone is replaced by another cone, whose height
3
is 1 cm and the radius of whose base is 2 cm, find
4
the drop in the water level.
​

Answer 1

Step-by-step explanation:

Let r be the radius of the cylindrical vessel, r=27.

Let r1 be the radius of the cone, r1=227=47.

The volume of water is equal to the difference in the volume of cylindrical vessel and the volume of cone.

V1=π(27)2×8−31×π(47)2×8

=722×(27)2×8−31×722×(47)2×8

=3847cm3

Therefore, the volume of water required to fill the vessel is 3847cm3.

As the cone is replaced by new cone which has the radius as 2 cm and height as