Question : A solid metallic sphere of radius 13 cm is melted and recast into a cone having a diameter of the base as 13 cm. What is the height of the cone?
Option 1: 246 cm
Option 2: 152 cm
Option 3: 174 cm
Option 4: 208 cm
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Correct Answer: 208 cm
Solution : We know, The volume of a cone = $\frac{1}{3}πr^2h$, where r is the radius of the cone The volume of a sphere = $\frac{4}{3}πR^3$, where r is the radius of the sphere According to the question, $\frac{4}{3}πR^3 = \frac13πr^2h$ Let the height of the cone be h ⇒$\frac{4}{3}π(13)^3 = \frac13π(\frac{13}{2})^2h$ ⇒ $h = 4 × 13^3 × (\frac{2}{13})^2$ ⇒ $h = 16 × 13$ ⇒ $h = 208$ cm ⇒ Height of the cone = 208 cm Hence, the correct answer is 208 cm.
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