Answer

Verified

381.6k+ views

**Hint:**In this particular question use the concept that the volume of the spherical steel ball is equal to the volume of the 8 new identical balls and the volume of the sphere is \[\dfrac{4}{3}\pi {r^3}\], so use these concepts to reach the solution of the question.

__Complete step-by-step answer__:Consider a spherical steel ball with center O having radius R is shown in the above figure.

Now this spherical steel ball is melted into 8 new identical balls, one of the new steel balls is shown in the above figure having center O’, and radius r.

Now as we know that the volume of the sphere is \[\dfrac{4}{3}\pi {R^3}\] cubic units, where R is the radius of the spherical ball.

As we know that when we melted the spherical steel ball to make 8 new identical balls the volume remains constant.

So the volume of the big spherical ball = volume of the 8 new spherical balls.

$ \Rightarrow \dfrac{4}{3}\pi {R^3} = 8\left( {\dfrac{4}{3}\pi {r^3}} \right)$

Where R is the radius of the big spherical steel ball and r is the radius of the new spherical steel balls.

Now simplify it we have,

\[ \Rightarrow {R^3} = 8\left( {{r^3}} \right)\]

\[ \Rightarrow {r^3} = \dfrac{{{R^3}}}{8}\]

\[ \Rightarrow {r^3} = \dfrac{{{R^3}}}{{{2^3}}}\]

Now take cube root on both sides we have,

\[ \Rightarrow r = \sqrt[3]{{\dfrac{{{R^3}}}{{{2^3}}}}} = \dfrac{R}{2}\]

**So the radius of the new balls is half of the radius of the original spherical steel balls.**

**Note**: Whenever we face such types of questions the key concept we have to remember is that always recall the when we melted something to make a new thing volume always remain constant and always recall the formula of the volume of the sphere which is stated above so simply equate the volume of the original spherical steel ball with the volume of the 8 new identical balls as above and simplify we will get the required radius of the new ball in terms of original ball.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Why is the adrenaline hormone called fight or flight class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between lanthanoids and actinoids class 12 chemistry CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples of unisexual and bisexual flowers

Open circulatory system is present in I Arthropods class 12 biology CBSE

Name the highest peak of the Indian Himalayas class 8 social science CBSE