Concept explainers
The density when the radius of an under-inflated volleyball increased by 10%

Answer to Problem 1TP
The correct answer is option e.
Explanation of Solution
Given info:
The radius of volleyball increases by 10%.
Formula used:
Density is mass per unit volume of the substance and is numerically given as
Calculation:
When radius of volleyball is increased by ten percent it means its volume increases.
The volume of sphere is given by
Initially volleyball's density can be given as
Neglected mass of air inside the ball
Substitute
Now when radius of ball increased by 10%, then new radius of ball is given as
Therefore, new volume of ball is
Substitute
Final volleyball's density can be given as
Neglected mass of air inside the ball
Substitute
Thus, change in density is,
=
Negative sign shows that density if volleyball's decreases.
In percentage this decrease can be given as
The density will decrease by approximately 25%.
Hence, the correct answer is option e and the options a, d, c, and d are incorrect.
Conclusion:
The density will decrease by approximately 25%.
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