Question

An ice cream pot has a right circular cylindrical shape. The radius of the base is 12 cm and the height is 7 cm. This pot is completely filled with ice cream. The entire ice cream is given to the students in the form of right circular ice cream cones, having a diameter of 4 cm and a height is 3.5 cm. If each student is given one cone, how many students can be served?

Answer 1

Given:

Ice Cream Pot:

Shape: Right circular cylinder

Radius of base = 12 cm

Height = 7 cm

Volume of the pot = Volume of cylinder

Ice Cream Cones:

Shape: Right circular cone

Diameter = 4 cm ⟹ Radius = 2 cm

Height = 3.5 cm

Volume of one cone = Volume of cone

Volume of the cylindrical ice cream pot:

Vcylinder​ = πr2h

= π(12)2 × 7

= π × 144 × 7

= 1008 π cm3

Volume of one cone:

Vcone​ = `1/3 pir^2h`

`= 1/3 pi(2)^2xx3.5`.

`= 1/3 pixx4xx3.5`

`=14/3 pi cm^3`

Number of students = `"Total volume"/"Volume per cone"`

Number of students = `(1008pi)/(14/3 pi)`

`= 1008/(14/3)`

`= 1008 xx 3/14`

`=3024/14`

= 216