Home
Class 10
MATHS
Three spheres of radius 'r' are kept ins...

Three spheres of radius 'r' are kept inside a cuylinder such that two of the speres are at bottom touching each other and sides of the cylinder while the third sphere is touching the two bottom spheres and the top of the cylinder .Find the volume of the cylinder .

Text Solution

Verified by Experts

By Pythagoras theorem,
AM=`r(sqrt(3))`
Height of cylinder H=`r+r(sqrt(3))+r rarr r(2+(sqrt(3)))`
Radius of cylinder R= 2r
Volume of cylinder `=piR^(2)H`
`=pi(2r^(2)).r(2+(sqrt(3)))=4pir^(3)(2+(sqrt(3)))`

Promotional Banner

Topper's Solved these Questions

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/exemplar|10 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN|Exercise Exercise|68 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Questions|4 Videos

Similar Questions

Explore conceptually related problems

Three spheres of radius 'r' are kept inside a cylinder such that two of the spheres are at bottom touching each other and sides of the cylinder while the third sphere is touching the two bottom spheres and the top of the cylinder.Then the volume of the cylinder is :

The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the cylinder, then the ratio of the rates of increase of the volume of the sphere and the volume of the cylinder, is

As shown in the adjacent figure, a sphere is placed in a cylinder. It touches the top, bottom and the curved surface of the cylinder. If radius of the base of the cylinder is 'r', (i) what is ratio of the radii of the sphere and the cylinder? (ii)what is the ratio of the curved surface area of the cylinder and the surface area of the sphere? (iii) what is the ratio of the volumes of the cylinder and the sphere?

A sphere and a cylinder have equal volume and equal radius. The ratio of the curved surface area of the cylinder to that of the sphere is