If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6cm, then how much water flows out of the cylindrical cup(a) 38.8c{{m}^{3}}(b) 55.4c{{m}^{3}}(c) 19.4c{{m}^{3}}(d) 471.4c{{m}^{3}}
To solve this problem, we need to calculate the volume of water displaced by the marble when it is submerged in the cylindrical cup. The volume of the displaced water will be equal to the volume of the marble.
Step 1: Find the volume of the marble. The marble is a sphere, so we use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * r³
Given the radius of the marble, r = 2.1 cm, we substitute it into the formula:
Volume of marble = (4/3) * π * (2.1)³ = (4/3) * π * (9.261) ≈ 38.8 cm³
Step 2: Water displaced The volume of water displaced by the marble is equal to the volume of the marble. Therefore, the amount of water that flows out of the cylindrical cup is 38.8 cm³.
Answer: (a) 38.8 cm³
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