A spherical ball of radius 3cm is melted and recast into 3 spherical balls. The radii of two of these balls are 1.5cm and 2cm. Find the radius of the third ball.
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the volume of bigger ball is equals to volume of smaller three balls ..
so , volume of sphere = 4/3πr^3
let radius of bigger original sphere is R
and radii of small spheres be r1 , r2. , r3
so ,
4/3πR^3 = 4/3πr1^3 + 4/3πr2^3 + 4/3πr3^3
4/3πR^3 = 4/3π ( r1^3 + r2^3 + r3^3 )
R^3 = r1^3 + r2^3 + r3^3
3^3 = 1.5^3 + 2^3 + r3^3
27 = 3.375 + 8 + r3^3
27 = 11.375 + r3^3
r3^3 = 27 - 11.375
r3^3 = 15.625
taking cube root of both sides
r3 = 2.5 cm
so , volume of sphere = 4/3πr^3
let radius of bigger original sphere is R
and radii of small spheres be r1 , r2. , r3
so ,
4/3πR^3 = 4/3πr1^3 + 4/3πr2^3 + 4/3πr3^3
4/3πR^3 = 4/3π ( r1^3 + r2^3 + r3^3 )
R^3 = r1^3 + r2^3 + r3^3
3^3 = 1.5^3 + 2^3 + r3^3
27 = 3.375 + 8 + r3^3
27 = 11.375 + r3^3
r3^3 = 27 - 11.375
r3^3 = 15.625
taking cube root of both sides
r3 = 2.5 cm
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