A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm.Such that it touhces the bottom .Find the volume of water of left in the cylinder, if the radius of the cylinder is equal to the radius to the cone.

Options

A. `642500 pi cm^(3)`
B. `642200 pi cm^(3)`
C. `648000 pi cm^(3)`
D. None

Answer

C

Explanation

(i) Whenever we placed a solid right circular cone in a right circular cylinder with full of water, then volume of a solid right circular cone is equal to the volume of water falled from the cylinder.
(ii) Total volume of water in a cylinder is equal to the volume of the cylinder.
(iii) Volume of water left in the cylinder = Volume of the right circular cylinder - Volume of a right circular cone.
Now, given that
Height of a right circular cone = 120 cm
Radius of a right cicrular cone = 60 cm
`therefore ` Volume of a right circular cone `= (1)/(3) pi r^(2) xxh`
`" " = (1)/(3) xx (22)/(7)xx 60 xx 60 xx 120`
`,, = (22)/(7) xx 20 xx 60 xx 120`
`= " " 144000 pi cm^(3)`
`therefore ` Volume of a right cicrular cone = Volume of water falled from the cylinder
`,, =144000 pi cm^(3)" "["from point(i)"]`
Given that, height of a right circular cylinder = 180 cm
and radius of a right circular cylinder = Radius of a right circular cone = 60 cm
`therefore` Volume of a right cirular cylinder `= pir^(2) xx h`
`" " = pi xx 60xx60xx180`
`" "= 648000 pi cm^(3)`
So, volume of a right cylinder = Total volume of water of water in a cylinder
`" "= 648000 pi cm^(3) " "["form point(ii)"]`