Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into 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  = $\frac{1}{3} \pi r^{2} h$
      
                              = $\frac{1}{3}$ × $\frac{22}{7}$ × (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  = $\frac{4}{3} \pi r^{3}$
 
                              = $\frac{4}{3}$ × $\frac{22}{7}$ × r³



$\frac{4}{3}$ × $\frac{22}{7}$ × r³ = 38.808 cm³

r³  =  $\frac{38.808 * 3 *7}{4*22}$
          
     = 9.261 

r = ∛ 9.261 
 
  = 2.1 cm

Radius of sphere = 2.1 cm

Answer 2

A cone is 8.4 cm high and the radius of its base is 2.1 cm. 

dimensions of the cone 

height(h) = 8.4cm

radius(r)= 2.1cm

we know that volume of the cone(V) = 1/3πr2h.

                                                     V=1/3*22/7*(2.1)^2*8.4
                      
                                                   V= 38.808 cubic cm.

cone is melted and recast into sphere.

so, the volume of the cone = the volume of the sphere.

we know that volume of the sphere= 4/3 π r3

                                                   V= 4/3*22/7*r3 cubic cm

so, the volume of the cone = the volume of the sphere.
we got the volume of the cone=38.808 cubic cm

4/3*22/7*r3 = 38.808

r3=(38.808*7*3)/4*22
   
   =9.261

r=cube root of 9.261

r=2.1cm

hence the radius of the sphere = 2.1cm

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