Question

A cylindrical container is filled with ice cream whose diameter is 8 cm and height is 15 CM the whole ice cream is distributed to 10 children in equal cones filled making hemispherical tops if the height of conical portion is 4 times its radius of its base find the radius of the ice cream cone

Answer 1

Answer:

The radius of the cone is approximately 2.289 cm

Step-by-step explanation:

Let's calculate the volume of the ice cream.

The volume of the cylinder = πr²h

r = 8/2 = 4 cm

Doing the substitution we have:

Vol = π × 4² × 15 = 240π

The ice is distributed to 10 children in cones.

The volume of each cone is:

= 240π/10 = 24π cm³

The cones have a conical part and a hemispherical top.

The volume of a cone = 1/3πr²h + 2/3πr³

Now, the height of the cone is four times the radius. so, we have:

h = 4r

Doing the substitution we have:

Vol = 1/3πr² × 4r + 2/3πr³

= 4/3πr³ + 2/3πr³ = 6/3πr³ = 2πr³

The volume of each cone = 24π cm³

Equating the two we have:

24π = 2πr³

r³ = 12

r = ∛12 = 2.289 cm

The radius of the cone is approximately 2.289 cm