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

Height of cone = 8.4cm
Radius of the cone = 2.1cm
Volume of the cone = 1/3 x 22/7 x 2.1 x 2.1 x 8.4
=22 x 2.1 x 0.7 x 1.2
=46.2 x 0.84
38.808cm³

Volume of cone = Volume of Sphere

38.808 = 4/3 x π x r³
38.808 = 4/3 x 22/7 x r³
38.808 x 3 x 7 / 4 x 22 = r³
9.26 = r³
3 = r

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 !!