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
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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
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