Q7 of 67 Page 195

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.

The cone, hemisphere and cylinder stand on equal bases which means their base radius is same


Let that base radius be r


It is given that height = r


Volume of cone = πr2h = πr3


Volume of hemisphere = πr3


Volume of cylinder = πr2h =πr3


Ratio of cone to hemisphere = =


Ratio of hemisphere to cylinder = =


⇒ ratio of volumes of all three solid = 1:2:3


More from this chapter

All 67 →
5

The volume of a cone is 308 cm3. Its height is 6 cm. The radius of its base is—

 6

The diameter of a solid metallic hemisphere is 42 cm. Find the cost of polishing its total surface at 20 paise per square cm.

 8

The left part of a solid is in the shape of a cylinder while the right part is in the shape of cone. The diameter of cylinder is 14 cm and height is 40 cm while the diameter of the conical part is 14 cm and height is 12 cm. Find the volume of the solid.

 9

Find the number of cones of radius 3 cm and height 6 cm that can be made by melting a metallic sphere of radius 9 cm.