Q. 164.1( 30 Votes )

# A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice-cream cone.

Answer :

Radius of cylindrical container = r = 6 cm

Height of cylindrical container = h = 15 cm

Volume of cylindrical container = πr^{2}h

= 22/7 × 6 × 6 × 15 cm^{3}

= 1697.14 cm^{3}

Whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops.

Let the radius of hemisphere and base of cone be r’

Height of cone = h = 4 times the radius of its base

h’ = 4r’

Volume of Hemisphere = 2/3 π(r’)^{3}

Volume of cone = 1/3 π(r’)^{2}h’ = 1/3 π(r’)^{2} × 4r’

= 2/3 π(r’)^{3}

Volume of ice-cream = Volume of Hemisphere + Volume of cone

= 2/3 π(r’)^{3} + 4/3 π(r’)^{3} = 6/3 π(r’)^{3}

Number of ice-creams = 10

∴ total volume of ice-cream = 10 × Volume of ice-cream

= 10 × 6/3 π(r’)^{3} = 60/3 π(r’)^{3}

Also, total volume of ice-cream = Volume of cylindrical container

⇒ 60/3 π(r’)^{3} = 1697.14 cm^{3}

⇒ 60/3 × 22/7 × (r’)^{3} = 1697.14 cm^{3}

⇒ (r’)^{3} = 1697.14 × 3/60 × 7/22 = 27 cm^{3}

⇒ r = 3 cm

∴ Radius of ice-cream cone = 3 cm

Rate this question :

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.

RD Sharma - MathematicsThe largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left.

RD Sharma - MathematicsAn wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.

RD Sharma - Mathematics