a cylindrical container of radius 6 cm and height 15 cm is filled with 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 cone
Answers
Answer:
3 cm.
Step-by-step explanation:
Given, radius r = 6 cm and height h = 15 cm.
We know that volume of cylinder = πr²h
= π(6)²(15)
= 540 π. ----- (i)
Let the radius of the base of the cone be R cm, then the height of the cone = 4R{∴ height is 4 times the radius of its base}.
∴ Volume of 10 cylindrical cones of ice-cream with hemispherical tops:
= 10[1/3 * π * r² * 4r] + 10 * (2/3)πr³
= (40/3) πr³ + (20/3) πr³
= 20 πr³ cm³. ----- (ii)
On solving (i) & (ii), we get
⇒ 540π = 20 πr³
⇒ r³ = 27 cm
⇒ r = 3 cm.
Therefore, radius of the cone = 3 cm.
Hope it helps!
Volume of ice cream = 3.142 x 6² x 15 = 1696.68
Each child gets = 1696.68/10 = 169.668 cm³
Take radius of cone = r = radius of hemisphere
Height of cone is therefore = 4r
Volume of hemisphere + volume of cone = 169.668 cm³
2/3 x 3.142 x r³ + 1/3 x 3.142 x r² (4r) = 169.668
2.09r³ + 4.19r³ = 169.668
6.28r³ = 169.668
r³ = 27
r = 3 cm
∴ Radius of cone = 3 cm