Answer :
Final answer:
The volume of water that overflows when a marble with a radius of 2.1 cm is placed in a cup is found by calculating the volume of the marble using the formula 4/3 πr³. The volume of the marble is 38.8 cm³, which is also the volume of water displaced and thus the amount that overflows.
Explanation:
To determine how much water overflows when a marble is placed into a cylindrical cup, we must calculate the volume of water displaced by the marble. The volume of the marble (which is a sphere) can be calculated using the formula for the volume of a sphere: V = 4/3 πr³, where r is the radius.
For a marble with a radius of 2.1 cm, the volume is:
V = 4/3 π(2.1 cm)³ ≈ 38.8 cm³
This is the volume of water that will be displaced and, as a result, overflow from the cup.
Therefore, the correct answer is (a) 38.8 cm³.
