A spherical steel ball is melted to make eight new identical balls. Then, the radius of each new ball be 1/8th the radius of the original ball. Write ‘True’ or ‘False’ and justify your answer

Solution:

Consider r as the radius of the original steel ball

r1 as the radius of the new ball which is formed after melting

From the question

Volume of original steel ball = 8 × Volume of eight identical balls

4/3 πr³ = 8 × 4/3 πr1³

By further simplification

r1 = r/2

Therefore, the statement is false.

✦ Try This: A spherical ball of radius 3 cm is melted and recast into three spherical balls.The radius of the two of the balls are 1.5 cm and 2 cm respectively. Determine the diameter of the third ball.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.2 Sample Problem 2

A spherical steel ball is melted to make eight new identical balls. Then, the radius of each new ball be 1/8th the radius of the original ball. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “A spherical steel ball is melted to make eight new identical balls. Then, the radius of each new ball be 1/8th the radius of the original ball” is false

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