Consider eight little spheres of mercury, each with a diameter of 1 millimeter. When they coalesce to form a single sphere, how big will it be? How does its surface area compare to the total surface area of the previous eight little spheres?
Size of the combined singlesphere and total surface area in compare to all littlesphere.
Answer to Problem 50A
The combined single sphere is twice the diameter of the little sphere and the total surface area is half of the surface area of eight little spheres.
Explanation of Solution
Given:
Number of littlespheres,
Diameter of a littlesphere,
Formula Used:
The volume of sphere is,
Where,
The total surface area of sphere is,
Where,
Calculation:
Volume of a littlesphere,
And volume of a combined single sphere,
The volume of the combined singlesphere will be equal to the volume of the all littlespheres.
So,
It means the single sphere will be twice of the diameter of the little sphere.
Now,
The total surface area of littlesphere is,
While the total surface area of the combined singlesphere is,
So,
Conclusion:
Therefore, the combined single sphere is twice the diameter of the little sphere and the total surface area is half of the eight littlespheres.
Chapter 18 Solutions
Conceptual Physics: The High School Physics Program
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