A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of sphere.
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radius of. the sphere is 2.1 cm
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Hi there !!
Cone
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Height , h = 8.4 cm
Radius , r = 2.1 cm
Volume of a cone =
= × × (2.1)² × 8.4
= 38.808 cm³
When the cone is melted ; its volume will remain the same.
This means that ,
Volume of cone = Volume of sphere
Volume of sphere = 4/3πr³
= 4/3 × 22/7 × r³
4/3 × 22/7 × r³ = 38.808 cm³
r³ = [ 38.808 × 7 × 3 ] ÷ [ 22 × 4 ]
= 9.261
r = ∛ 9.261
= 2.1 cm
Radius of sphere = 2.1 cm
Hope the answer is helpful !!
Good Day !!
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