Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A solid metallic sphere of radius 13 cm is melted and recast into a cone having diameter of the base as 13 cm.
Concept used:
Volume of a cone = 1/3πr2h
Volume of a sphere = 4/3πr3
Calculation:
According to the question,
4/3πr3 = 1/3πr2h
Let height of the cone be h
So,
4 × 133 = (13/2)2 × h
⇒ h = 4 × 133 × (2/13)2
⇒ h = 16 × 13
⇒ h = 208
So, height = 208 cm
∴ The required answer is 208 cm.
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