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A solid metallic sphere of radius 105 cm is melted and recast into a number of smaller cones, each of radius 35 cm and height 3 cm. Find the number of cones so formed. |
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Answer» Let R be the radius of solid sphere \(\therefore\) R = 10.5 cm Also let r & h be the radius and height of formed each smaller cones respectively. \(\therefore\) r = 3.5 cm & h = 3 cm \(\therefore\) Total number of cones so formed = \(\frac{volume\,of\,shpere}{volume\, of \, one\, cone}\) ⇒ n = \(\cfrac{\frac43\pi R^3}{\frac13\pi r^2h}\) = \(\frac{4R^3}{r^2h}\) = \(\frac{4\times10.5\times10.5\times10.5}{3.5\times3.5\times3}\) = 12 x 10.2 = 126 Hence, number of cones so formed = 126 |
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