The surface area of a solid metallic sphere is 616 cm2. It is melted a

1.	The surface area of a solid metallic sphere is 616 cm2. 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» 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

The surface area of a solid metallic sphere is 616 cm2. 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»

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