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Answer :
Final answer:
The volume of a marble of radius 2.1 cm is calculated using the formula for the volume of a sphere, leading to a displaced water volume of 38.8 cm³, hence, that is how much water overflows from the cylindrical cup.
Explanation:
When a marble is submerged in water, it displaces a volume of water equal to its own volume. Therefore, to find out how much water flows out of the cylindrical cup, we need to calculate the volume of the marble.
The volume of the marble (sphere) can be calculated using the formula:
V = ⅔πr³
Where V is the volume of the sphere, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the marble.
Using the radius of the marble (2.1 cm), the formula becomes:
V = ⅔π(2.1 cm)³ = ⅔π(9.261 cm³) = 38.8 cm³
Thus, the answer to how much water will flow out when the marble is placed into the water-filled cylinder is 38.8 cm³, which corresponds to option (a).
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