Question
A solid metallic sphere of radius 15 cm is melted and
recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all the balls?Solution
Let the number of the smaller sphere be 'x' Volume of the bigger sphere = x × (volume of the smaller sphere) (4/3)π 15^3 = x × (4/3)π 3^3 x = 125 So their are total 125 smaller spheres Now, The surface area of the larger sphere = 4π 15 ⇒ 900π Surface area of smaller sphere = 4π 3^2 ⇒ 36π Total surface area of 125 smaller spheres = 125 × 36π ⇒ 4500π Surface area of the bigger sphere : Surface area of all smaller spheres = 900π : 4500π ⇒ 1 : 5
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