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A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone. |
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Answer» Volume of a sphere = \(\frac{4}{3}\)πr3 Volume of a cylinder = \(\frac{1}{3}\)πr2h Given, radius of the internal and external surfaces of a hollow spherical shell are 2 cm and 4 cm respectively. It is melted into a cone of base radius 4 cm. ⇒ Volume of material in sphere = Volume of the cone ⇒ \(\frac{4}{3}\)x π x (43 - 23) = \(\frac{1}{3}\)π x 42 x h ⇒ h = 14 cm L2 = h2 + r2 ⇒ l = \(\sqrt{14^2+4^2}\) ⇒ l = \(\sqrt{212}\) = 14.56 cm |
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