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

radius of sphere is 2.1
volume of cone= volume of sphere
1/3*22/7*2.1*2.1*8.4=4/3*22/7*r3
r3= (2.1)3
r=2.1

Answer 2

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

Hope the answer is helpful !!

Good Day !!