Question

a right circular cone is of height 8.4 cm and radius of its base is 2.1 cm It is melted and recast into spare find the radius of the sphere​

Answer 1

we know that: 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.

Vc= Vs;

πR²h/3= 4πr³/3;π×2.1²×8.4/3=4πr³/3;

38.808 = 4πr³/3;

3×38.808=4πr³/3;

4πr³=116.424;

r³=116.424/4π;

r³ = 9.261;

r = ∛9.261;

r = 2.1 cm

So, the radius of the sphere is 2.1 cm

bye :-)

Answer 2

EXPLANATION.

Right circular cone of height = 8.4 cm.

Radius of its base = 2.1 cm.

It is melted and recast into sphere.

As we know that,

Volume of a cone = 1/3πr²h.

Volume of sphere = 4/3πr³.

Using this formula in the equation, we get.

Volume of cone = Volume of sphere.

⇒ 1/3πR²h = 4/3πr³.

⇒ πR²h = 4πr³.

⇒ R²h = 4r³.

⇒ (2.1)² x 8.4 = 4 x r³.

⇒ 4.41 x 8.4 = 4 x r³.

⇒ 37.044 = 4 x r³.

⇒ r³ = 9.261.

⇒ r³ = (2.1)³.

⇒ r = 2.1 cm.

Radius of sphere = 2.1 cm.