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A metal sphere is melted and re-casted into a cone. Both have same radiia. Find the relationship between the height of the cone and the radius of the sphere.b. Which solid has greater surface area? Justify. |
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Answer» a. If r is the radius of the sphere, then its volume = \(\frac{4}{3}\) πr3 If h is the height of the cone, then its volume = \(\frac{1}{3}\pi r^2h\) = \(\frac{4}{3}\pi r^3\) h = 4r Height of pyramid is four times the radius of sphere. Surface area of the sphere = 4πr2 Slant height of the cone = \(\sqrt{(4r)^2+r^2}\) = \(\sqrt{17r^2}\) = \(\sqrt{17r}\) Surface area of the cone = \(\pi r^2+\pi r\sqrt{17r}\) = \(\pi r^2(1+\sqrt{17})\) b. Surface area of the cone is greater |
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