(Q4)A cylindrical container is filled with ice-cream whose diameter is 12 cm and height is 15 cm. The whole ice cream is distributed to 10 children by filling in equal cones and forming hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice cream cone.

4x cmx cmx cm

Let the radius of the base of conical ice cream = x cm

∴ diameter = 2x cm

Then, the height of the conical ice cream = h = 2(diameter) = 2(2x) = 4x cm

Volume of ice cream cone = Volume of conical portion + Volume of hemispherical Portion.

=
1
3
πr2h +
2
3
πr3
=
1
3
πx2( x) +
2
3
πx3
=
πx3 + 2πx3
3
=
πx3
3

= πx3

Diameter of cylindrical container = 12cm

Its height (h) = 15cm

∴ Volume of cylindrical container = πr2h

= π( )2

= π cm3

Number of children to whom ice cream is given = 10

Volume of cylindrical container
Volume of one icecream cone
= 10
π
2πx3
= 10

⇒ 2πx3 × 10 = π

x3 =
2 × 10
=

⇒ x3 =

⇒ x =

∴ Diameter of ice cream cone 2x = 2( ) = cm.