The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed .(Use π=22/7)
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Base diameter of the cone = 14 cm
Step-by-step explanation:
Given: Surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm.
To Find: Diameter of the base of the cone so formed.
Solution:
Surface area of sphere = 4πr² = 616
4 * 22/7 * r² = 616
r² = 616 * 7 / 88
r = root of 49 = 7cm
Radius of the sphere = 7 cm
Volume of the sphere = 4/3πr³ = 4/3π(7)³ cu.m.
Volume of the cone = πR²H/3
πR²H/3 = 4/3π(7)³
R²*28 = 4(7)³
R² = 4 * 7 * 7 *7 / 28 = 49 = 7cm
Base diameter of the cone = 14 cm
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