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A metal sphere of radius 12 centimetres is melted and recast into 27 small spheres. What is the radius of each sphere? |
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Answer» Radius = 12cm Volume of bigger sphere = \(\frac{4}{3}\pi R^3=\frac{4}{3}\pi \times12^3\) If the radius of smaller sphere is ‘r’ Volume of 27 smaller spheres = Volume of the bigger sphere \(27\times\frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3\) \(27\times\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times12^3\) 27r3 = 123 \(r^3=\frac{12^3}{27}=\frac{1728}{27}=64\) r3 = 64 Radius of smaller sphere = 4 cm |
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