Question : A solid metallic sphere of radius 12 cm is melted and recast into a cone having a diameter of the base of 12 cm. What is the height of the cone?
Option 1: 258 cm
Option 2: 192 cm
Option 3: 166 cm
Option 4: 224 cm
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Correct Answer: 192 cm
Solution :
According to the question,
The volume of the sphere = Volume of the cone
So, $\frac{4}{3}\pi12^3= \frac{1}{3}\pi6^2h$
⇒ $4 × 12^3 = \pi6^2h$
⇒ $4 \times 48 = h$
⇒ $h = 192$
Hence, the correct answer is 192 cm.
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