A geometry problem by Sudhagar` M
Geometry
Level
2
Three spherical balls of radius 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is
3 cm
5 cm
6 cm
2 cm
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1 solution
Volume of the new ball = (3/ 4). (4/3) (r^{3}1.r^{3}2 .r^{3}3)
= (1^{3}+ 2^{3} + 3^{3})
= (1 + 8 + 27)
= 36p cubic cm.
(4/3) r^{3} = 36
r^{3} = (36 x 3)/4 = 27