A solid metal ball of radius 3cm is melted and the metal obtained is recast to form a solid circular cone of radius 4cm. Find the height of the cone.
Answers
Answer:
answer is 6.75 cm which is required height ... see solution on page i aploaded
Height of the resultant cone = 6.75 cm
Given:
A solid metal ball of radius 3 cm is melted and the metal obtained is recast to form a solid circular cone of radius 4cm.
To find:
The height of the cone
Solution:
Given Radius of solid ball r = 3 cm
As we know
Volume of sphere = (4/3) π r³
Volume of sphere = (4/3) (22/7) 3³ = 4(22/7) 3²
After melting the metal obtained is recast to form a solid circular cone.
Then the volume of metal = 4(22/7) 3²
Radius of the resultant cone = 4 cm
As we know
Volume of cone = (1/3) π r² h
Where h = height of the cone
Then volume of the resultant cone = (1/3) (22/7) 4²h
We know that volume of melted metal and volume of cone will be equal
⇒ 4(22/7) 3² = (1/3) (22/7) 4²h
⇒ 4(3³) = 4²h
⇒ 27 = 4h
⇒ h = 6.75
Therefore, Height of the resultant cone = 6.75 cm
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