Question

A cylindrical container is filled with ice-cream, whose diameter is 10cm and the height 17.5cm. The whole ice-cream is distributed to 12 children in equal cones having hemispherical tops. If the height of the conical portion is five times the radius of it's base, find the diameter of the ice-cream cone.

Answer 1

The diameter of the ice-cream cone is 3.718 cm

Step-by-step explanation:

Diameter of cylindrical container = 10 cm

Radius of cylindrical container = $\frac{10}{2}=5 cm$

Height of cylinder = 17.5 cm

Volume of cylindrical container = $\pi r^2 h$

Volume of cylindrical container = $\frac{22}{7} \times 5^2 \times 17.5$

Volume of cylindrical container = $1375 cm^3$

The whole ice-cream is distributed to 12 children in equal cones having hemispherical tops

So, Amount of ice cream for 1 student =$\frac{1375}{12}$

Amount of ice cream for 1 student =$114.583 cm^3$

Let the radius of hemisphere be r

The height of the conical portion is five times the radius of it's base

Height of conical portion = 5r

Volume of 1 cone = Volume of cone+ Volume of hemisphere

Volume of 1 cone = $\pi r^2 h +\frac{2}{3} \pi r^3$

Volume of 1 cone = $\pi r^2 (5r) +\frac{2}{3} \pi r^3$ ---A

Amount of ice cream for 1 student =$114.583 cm^3$ --B

So, Equate A and B

$\pi r^2 (5r) +\frac{2}{3} \pi r^3=114.583$

$\frac{22}{7} \times r^2 (5r) +\frac{2}{3} \times \frac{22}{7} r^3=114.583$

$r=1.859$

So, Radius of cone is 1.859 cm

Diameter = $2 \times r = 2 \times 1.859 = 3.718$

Hence the diameter of the ice-cream cone is 3.718 cm

#Learn more :

A cylindrical container whose diameter is 12 cm and height is 15 cm is filled with ice- cream. Ice-cream is distributed to ten children in equal cones having hemispherical tops. If the height of conical portion is twice the diameter of its base, find the diameter of the ice-cream cone.

https://brainly.in/question/8818366