Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere.
Given :
r1= 6cm, r2= 8cm, r3= 10 cm
Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³
Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³
Volume of third metallic sphere (V3) = 4/3π(r3)³ = 4/3 π (10)³
Volume of single solid sphere(V)= 4/3πR³
A .T.Q
Volume of 3 metallic spheres= volume of single solid sphere
V1+V2+V3 = V
4/3 π (6)³+ 4/3 π (8)³+4/3 π (10)³= 4/3πR³
4/3π(6³+8³+10³) = 4/3 πR³
216+ 512+ 1000 = R³
1728= R³
(12×12×12) = R³
12³= R³
R= 12
Hence, the radius of the resulting sphere = 12 cm
================================================================
Hope this will help you....
