If a marble of radius 2.1 cm is put into a cylindrical cup of radius 6cm and height 8cm, then how much water flows out of it.?

38.8 cm

38.8cm3

To determine how much water flows out of the cylindrical cup when the marble is put into it, we need to calculate the volume of the submerged part of the marble.

The volume of a sphere is given by the formula:

V = (4/3)πr^3

Where:
V = volume of the sphere
π = pi (approximately 3.14159)
r = radius of the sphere

Given that the radius of the marble is 2.1 cm, we can substitute this value into the formula:

V = (4/3)π(2.1)^3

V ≈ 4.18879 × 9.261

V ≈ 38.79212 cm^3 (rounded to 5 decimal places)

Now, since the marble will displace an equal volume of water when submerged, the amount of water that flows out of the cup is equal to the volume of the submerged part of the marble.

Therefore, the amount of water that flows out is approximately 38.79212 cm^3.

To find out how much water flows out of the cylindrical cup when the marble is put into it, we need to calculate the volume of the water displaced by the marble.

The volume of the marble can be calculated using the formula for the volume of a sphere:

V_marble = (4/3) * π * r^3

where r is the radius of the marble.

Given that the radius of the marble is 2.1 cm, we can substitute this value into the formula:

V_marble = (4/3) * π * (2.1 cm)^3

V_marble ≈ 39.598 cm³

Now, to find the volume of water displaced by the marble and flows out of the cup, we can subtract the volume of the marble from the volume of the cup.

The volume of the cup can be calculated using the formula for the volume of a cylinder:

V_cup = π * r^2 * h

where r is the radius of the cup and h is the height of the cup.

Given that the radius of the cup is 6 cm and the height is 8 cm, we can substitute these values into the formula:

V_cup = π * (6 cm)^2 * 8 cm

V_cup ≈ 904.778 cm³

Therefore, the volume of water that flows out of the cup when the marble is put into it is:

Volume of water = V_cup - V_marble
≈ 904.778 cm³ - 39.598 cm³
≈ 865.18 cm³

Hence, approximately 865.18 cm³ of water would flow out of the cup when the marble is put into it.