An ice cream seller has two types of ice cream container in the form of

cylindrical shape and a cone with hemi-spherical base. Both have same height

of 7 cm and same diameter of 7 cm. The cost of container are same but the

seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume

of the both containers. (ii) Which value is depicted by the seller?

The diameter of containers are 7 cm each and height 7 cm
The radius of the cylindrical container r = 7/2 = 3.5
The height of the cylindrical container h = 7 cm
The volume of cylindrical container = ​π r^​2h
                                                          = 22/7 x 3.5 x 3.5 x 7
                                                          = 269.5 cm³
For the Conical container with hemispherical base :-
The total height = 7 cm
The base diameter = 7 cm
The radius of the hemispherical part = 3.5 cm
The volume of hemispherical part = 2/3​πr³
                                                       = 2/3 x 22/7 x 3.5 x 3.5 x 3.5
                                                       = 296.5/3 cm³
The Height of the conical part h1 = 7 - 3.5 = 3.5
The volume of the conical part = 1/3π r² h1
                                                = 1/3 x 22/7 x 3.5 x 3.5 x 3.5
                                                = 134.75 / 3 cm³

Therefore ,
The volume of the 2nd type of container = Volume of hemispherical part + Volume of conical part
                                                                = 269.5 / 3 + 134.75 / 3
                                                                = 404.25 / 3
                                                                = 134.75 cm³
Since the volume of cylindrical container is more than the 2nd container, Thus it shows is honesty.