Question
Download Solution PDFA solid metallic sphere of radius 21 cm is melted and moulded into small right circular cones, each of radius 7 cm and height of 3 cm. The number of such cones is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of sphere = 21 cm
Radius of the base of small cones = 7 cm
Height of small cones = 3 cm
Formula used:
Volume of sphere = (4/3) × π × r3
Volume of cone = (1/3) × π × r2 × h
Where r = radius and h = height of cone
Calculation:
Let the number of small cones = N
The volume of each small cone × N = The volume of the sphere
⇒ N × (1/3) × π × r2 × h = (4/3) × π × r3
⇒ N × (7)2 × 3 = 4 × (21)3
⇒ N = 4 × 3 × 3 × 7
⇒ N = 252
∴ The correct answer is 252.
Last updated on Jun 12, 2025
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