Question
A solid metallic sphere of diameter 30 cm is melted and
recast into a right circular cone having diameter of the base equal to 15 cm. What is the height of the cone?Solution
Radius of the sphere = 30 ÷ 2 = 15 cm Volume of the sphere = 4/3 X 22/7 X 15 X 15 X 15 cm3 Let the height of the cone be 'h' cm. Now, volume of the sphere = volume of the cone So, 4/3 X (22/7) X 15 X 15 X 15 = 1/3 X 22/7 X (15/20 X (15/2) X h Or, 'h' = 4 X 2 X 2 X 15 So, 'h' = 240 Required height = 240 cm
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