Question

If a spherical steel ball is melted to make
27 new identical balls then the radius of each new ball is 1/27 th the radius of the original ball . State true and false with proper solution

Answer 1

According to me it is false

here is the explanation:

let r be radius of the new spherical ball and R be the radius of steel ball which is being melted to form other 27 ball
since there are 27 identical ball so
volume of the ball so formed will be equal to 1/27th of the volume of original ball

so,
4/3 π r^3 = 1/27(4/3 π R^3)
4/3 and π is being cancelled with each other.
so
r^3 = 1/27(R^3)
r =[1/27 (R^3)]^1/3. { hope you
understand this part}
so
r. = 1/3 R

so the given statement is false
the radius will be 1/3rd of the orignal radius.