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A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how much times the radius of the original ball​
  • a)
    1/3
  • b)
    1/4
  • c)
    1/2
  • d)
    1/8
Correct answer is option 'C'. Can you explain this answer?
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A spherical steel ball is melted to make 8 new identical balls. Then t...
To solve this problem, we need to use the concept of volume. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.

Let's assume the radius of the original ball is r. Therefore, the volume of the original ball is V₁ = (4/3)πr³.

When the original ball is melted to make 8 new identical balls, the total volume remains the same. So, the volume of each new ball is equal to V₁/8.

Let's assume the radius of each new ball is R. Therefore, the volume of each new ball is V₂ = (4/3)πR³.

Since the volume of each new ball is V₁/8, we have:

V₂ = V₁/8
(4/3)πR³ = (4/3)πr³/8

Simplifying the equation, we have:

R³ = r³/8
R = (r³/8)^(1/3)
R = r/2

Therefore, the radius of each new ball is half the radius of the original ball.

Hence, the correct answer is option c) 1/2.
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A spherical steel ball is melted to make 8 new identical balls. Then the radius of each new ball is how much times the radius of the original balla)1/3b)1/4c)1/2d)1/8Correct answer is option 'C'. Can you explain this answer?
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