Solution:
(i)Given surface area of the solid metallic sphere = 1256 cm2
4R2 = 1256
4×3.14×R2 = 1256
R2 = 1256/4×3.14
R2 = 100
R = 10
Hence the radius of solid sphere is 10 cm.
(ii)Volume of the solid sphere = (4/3)R3
= (4/3)×103
= (4000/3) cm3
= 12560/3 cm3
Radius of the cone, r = 2.5 cm
Height of the cone, h = 8 cm
Volume of the cone = (1/3)r2h
= (1/3)×3.14×2.52×8
= 157/3 cm3
Number of cones made = Volume of the solid sphere/ Volume of the cone
= (12560/3)÷( 157/3)
= (12560/3)×( 3/157)
= 12560/157
= 80
Hence the number of cones made is 80.