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प्रश्न
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?
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उत्तर
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
