Question 21 (OR 2 nd   question)

A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of balls

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Question 21 (OR 2nd question) A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of balls Since the big sphere is melted to make balls Volume of big sphere = Volume of balls Volume of big sphere = Number of balls × Volume of 1 ball ∴ Number of balls = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑏𝑖𝑔 𝑠𝑝ℎ𝑒𝑟𝑒)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑏𝑎𝑙𝑙) Volume of big sphere Radius = 3 cm Volume of sphere = 4/3 𝜋(𝑟)3 = 4/3×𝜋×(3)^3 = 4/3×𝜋×27 Volume of 1 ball Diameter = 0.6 cm Radius = 0.6/2 = 0.3 cm = 3/10 cm Volume of 1 ball = 4/3 𝜋(𝑟)3 = 4/3×𝜋×(3/10)^3 = 4/3×𝜋×27/1000 Now, Number of balls = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑏𝑖𝑔 𝑠𝑝ℎ𝑒𝑟𝑒)/(𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 1 𝑏𝑎𝑙𝑙) = (4/3 × 𝜋 × 27" " )/(4/3 × 𝜋 × 27/1000) = 27" " /( 27/1000) = 27" " /27 × 1000 = 1000 ∴ Number of balls is 1000

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.