# Eight spheres of equal radii are obtained by melting a metallic sphere of radius 10 cm. Find the surface area of each sphere thus obtained.

Let the radius of small spheres formed be r2

Radius of sphere which is melted = r1 = 10 cm

As the sphere is melted and then the small spheres are made from the same amount of melted sphere, therefore, the volume remains same

Volume of sphere = πr3

8 × πr23 = πr13

8r23 = r13

Substituting values

8 × r23 = 103

8 × r23 = 1000

r23 =

r2 = = 5 cm

Surface area of sphere = 4πr2

surface area of small spheres made = 4πr22

= 4 × π × 52

= 4 × π × 25

= 100π cm2

Therefore, surface area of each sphere obtained is 100π cm2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Surface Area and Volume49 mins
Surface Area and Volumes43 mins
Quiz | Surface Area and Volumes42 mins
Champ Quiz | Area Related with the Circle45 mins
Quiz | Area Related with Circles47 mins
Short Cut Trick to Find Area of Triangle43 mins
Idioms and Phrases43 mins
Goprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and Nomenclature52 mins
Learn to Make Your Own Acid Rain and pH Paper at Home!27 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses