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The ratio of total surface area and volume of a sphere is 1 ∶ 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

The ratio of total surface area and volume of a sphere is 1 ∶ 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres? Correct Answer 33264

Total surface area/volume = 4πr2/(4/3πr3) = 1/7

⇒ r = 21 cm

⇒ Radius of small spheres = 21/6 cm

Let’s suppose large sphere is melted to form ‘n’ no. of small spheres,

⇒ 4/3π × 21 × 21 × 21 = n × 4/3π × 21/6 × 21/6 × 21/6

⇒ n = 216

∴ Curved surface area of all the smaller spheres = 216 × 4πr2

⇒ 216 × 4 × 22/7 × 21/6 × 21/6

⇒ 33264 cm2

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