a right circular cone of height 8.4cm and the radius of its base is 2.1cm .it is melted and recast into a sphere.find the radius of the sphere.
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Solution :-
As the right circular cone is melted and recast into a sphere, then the volume of cone will be exactly equal to the volume of sphere.
∴ Volume of cone = Volume of sphere
⇒ 1/3πr²h = 4/3πr³
⇒ 1/3*22/7*2.1*2.1*8.4 = Volume of sphere
⇒ 38.808 = 4/3*22/7*r³
⇒ 38.808 = 88/21*r³
⇒ 88r³ = 38.808*21
⇒ 88r³ = 814.968
⇒ r³ = 814.968/88
⇒ r³ = 9.261
⇒ r = ∛9.261
⇒ r = 2.1 cm
So, the radius of the sphere is 2.1 cm
Answer.
As the right circular cone is melted and recast into a sphere, then the volume of cone will be exactly equal to the volume of sphere.
∴ Volume of cone = Volume of sphere
⇒ 1/3πr²h = 4/3πr³
⇒ 1/3*22/7*2.1*2.1*8.4 = Volume of sphere
⇒ 38.808 = 4/3*22/7*r³
⇒ 38.808 = 88/21*r³
⇒ 88r³ = 38.808*21
⇒ 88r³ = 814.968
⇒ r³ = 814.968/88
⇒ r³ = 9.261
⇒ r = ∛9.261
⇒ r = 2.1 cm
So, the radius of the sphere is 2.1 cm
Answer.
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