Question

a solid sphere of radius R is melted and recast into shape of a solid cone of height are the radius of the base of a cone is​

Answer 1

The Radius of the base of the cone is 2r.

Step-by-step explanation:

Given :  

A solid sphere of radius =  r  

solid cone of height,h =  r

Let the radius of the cone be ‘R’  

Volume of sphere =  Volume of cone

[Sphere is melted and recast in the shape of cone]

4/3 πr³ =  ⅓ πR²h

4r³ = R²(r)

4r³/r = R²

4r² = R²

R = √(4r²)

R = 2r

Radius of the cone = 2r

Hence, the Radius of the cone is 2r.

Answer 2

Answer:

2r

Step-by-step explanation:

Volume of sphere = Volume of cone

R = radius of base of cone

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

Radius of sphere = h of cone

$4 {r}^{3} = {R}^{2} h$

$4 {r}^{3} = {R}^{2}$

$R = \sqrt{4 {r}^{2} }$

$R=2r$

Therefore, Radius of the base of the cone is double the radius of sphere (h of cone).