Question

a right cylindrical container of radius 6 and hieggt 15 is full of ice crem which has to distribute to 10 children in equal coned having hemispherical shape on the top if height of conical portion is four times its base radius find the radius of the ice cream cone

Answer 1

Solution:

Volume of Ice cream in the Cylindrical Container = πr²h

and  here r = 6 cm , h = 15 cm

= πr²h = 36×π15

now we will find the volume of each cone with hemispherical top

by formula we have

= 1/3πR²H +2/3πR³ = 1/3πR² (H+2R)

= 1/3 πx²(4x+2x)  , ∵ let the radius = x and height = 4x

= 2πx³

Now the volume of ice-cream in  container = 10× volume of each cone

36×15π = 20πx³

⇒ x³ = 36×15/20 = 27

∴ x = 3 hence radius of each ice cream is 3 cm.