Question

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 the sphere​

Answer 1

Answer:

2.1 cm

Step-by-step explanation:

Volume of the cone =31πrc2h

Volume of the sphere =34πrs3

rc is the radius of cone =2.1 cm        ....(Given)

Let rs be the radius of the sphere

h is the height of cone =8.4 cm        ...(Given)

Volume of cone = Volume of sphere          ...(Given)

⇒31πrc2h=34πrs3

⇒31rc2h=34rs3

⇒rs3=9.261

⇒rs=2.1 cm

I hope it helps you. :)

Answer 2

Answer:

2.1 cm

Step-by-step explanation:

Volume of cone = Volume of sphere

$\frac{1}{3} \pi r^{2} h$                   = $\frac{4}{3} \pi R^{3}$

$\frac{1}{3} \pi (2.1)^{2} 8.4$           = $\frac{4}{3} \pi R^{3}$

$2.1*2.1*8.4$        = $4R^{3}$

$( 2.1)^{3}$                    = $R^{3}$

$R$                          = $2.1$