Question

The surface area of a solid metallic sphere is 616 cm^2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed [use π = \(\frac{22}7\)].

Answer 1

Surface area of the sphere = 4πr²

⇒ 4πr² = 616 

⇒ 4 x \(\frac{22}7\) x r² = 616

⇒ r² = \(\frac{{616}\times{7}}{{4}\times{22}}\)

⇒ r² = 49 

⇒ r = \(\sqrt{4}9\) 

⇒ r = 7 cm 

Diameter of base = 7 × 2 

= 14 cm