Multiple choice

A solid metallic sphere of radius 13 cm is melted and recast into a cone having diameter of the base as 13 cm. What is the height of the cone?

  1. $246 cm$
  2. $152 cm$
  3. $174 cm$
  4. $208 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3)πr³ = (4/3)π(13)³. Cone has diameter 13 cm, so radius = 6.5 cm. Let height be h. Volume of cone = (1/3)πr²h = (1/3)π(6.5)²h. Equating volumes: (4/3)π(13)³ = (1/3)π(6.5)²h. Cancel (1/3)π: 4(13)³ = (6.5)²h. Note 6.5 = 13/2, so (6.5)² = (13)²/4. Substituting: 4(13)³ = ((13)²/4)h. Dividing both sides by (13)²/4: h = 4 × 4 × 13 = 16 × 13 = 208 cm.

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