Math, asked by horselover26, 10 months ago

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

Answered by arifawazir4
4

Answer:

answer is 6.75 cm which is required height ... see solution on page i aploaded

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Answered by Dhruv4886
2

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

#SPJ2

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