The surface area of a solid metallic sphere is 616 cm² . It is melted and recast into a solid cone of height 28 cm. Find the diameter of the base of the cone so formed. (Take π=22/7)

14 cm

We know that,

Surface area of sphere  = 4πr²

The volume of the sphere = \(\frac{4}{3}\)πR³

The volume of the cone =  \(\frac{1}{3}\)πR²H

We have,

Area of solid sphere = 616 cm² ,

Height of cone = 28 cm

4πr² = 616 cm²

then, r² =  49 

r = 7

Volume of sphere = volume of cone

= \(\frac{4}{3}\)πR³ =  \(\frac{1}{3}\)πR²H

=4r³ = R² H

by putting, r = 7 cm , H = 28 cm

= 4×(7)³ = R² × 28

R = 7

D = 14 cm