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 sphere.

Answer 1

Hi there !!

Cone 
------------

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

Answer 2

Cone 
------------

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