A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. [4 MARKS]
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Solution
Formula: 1 Mark Application: 1 Mark Solution: 2 Marks
External radius of the hollow sphere =82cm = 4 cm Internal radius of the hollow sphere =42cm = 2 cm ∴ Volume of the hollow sphere = Volume of external sphere - Volume of internal sphere =43π(4)3−43π(2)3=43π[43−23] =43π[64−8]=43π×56cm3……(i) Radius of the cone =82cm=4cm Let h be the height of the cone. Then, volume of the cone =13π(4)2h =13π×16hcm3……(ii) According to the question, 43π×56=13π×16h [From (i) and (ii)] ⇒h=4×5616cm=14cm