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The base radius and height of right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast into spheres of diameter 2 cm each. Find the number of sphere's so formed. - Surface areas and volumes.

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Please find below the solution to the asked query :

Radius of base of solid cone, R = 2 cmHeight of cone, h = 8 cmNow, volume of cone = 13πR2H = 13π22×8 = 32π3 cm3Diameter of 1 sphere, d = 2 cmradius, r = 1 cmVolume of 1 sphere = 43πr3 = 43π13 = 4π3 cm3Number of spheres obtained = volume of coneVolume of 1 sphere = 32π3 ÷ 4π3 = 32π3 × 34π = 8


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CONE:                SPHERE:
R= 2cm                d= 2cm 
H= 8cm                 r= 1cm 

Let the number of sphere's be  x
 :. Volume of cone = Volume of the total no. of sphere's 
     1/3 pi R2 H        =  (x) 4/3 pi r3  
                    R2H        =  (x)  4 r3
               2 X 2 X 8  =  (x) 4 X 1 X 1 X 1    
               4  X 8          =  x
                  4    
                 x= 8 spehere's 
THUMBS UP PLS ! 
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Let radius of cone (r1) = 2 cm
Let height of cone (h1) = 8 cm
Now,
Diameter of sphere = 2 cm
∴ It' radius (r2) = 1 cm
Let the no' of spheres formed = n
Now, according to the question
➡ 1/3 × πr12h1 = 4/3 × πr23 × n
➡ 1/3 × π × 4 × 8 = 4/3 × π × 1 × n
➡ n = 1/3 × π × 32 × 3/4 × 1/π
➡ n = 32/4
➡ n = 8
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