A graduated cylinder contains 56.3ml of water. A metal cylinder is dropped in the water and is completely covered by water. The diameter of the cylinder is 3.8 cm and the height of the cylinder in 5.4cm. What is the volume reading in the graduated cylinder after the cylinder is added?

add the volume of the cylinder, PI*r^2*h

r=1.9cm, h=5.4cm.

volume of metal = pi*r^2*h

pi you know.
r = 3.8/2 = ? cm
h = 5.4 cm
v = ? cc.

What ever the volume of the cylinder it will displace that much of the water so
final volume of water in graduated cylinder = 56.3 + volume metal.(all of this assumes the cylinder of metal is SOLID and not a hollow cylinder).

To find the volume reading in the graduated cylinder after the metal cylinder is added, we need to calculate the volume of the metal cylinder.

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the diameter is 3.8 cm, we can calculate the radius by dividing the diameter by 2:
r = 3.8 cm / 2 = 1.9 cm

Plugging in the values, we have:
V = π(1.9 cm)^2 * 5.4 cm

Calculating the volume gives:
V = 108.8 cm^3

Therefore, the volume reading in the graduated cylinder after the cylinder is added is 56.3 ml + 108.8 cm^3.

To find the volume reading in the graduated cylinder after the metal cylinder is added, we first need to calculate the volume of the metal cylinder.

Step 1: Calculate the radius of the metal cylinder.
The diameter is given as 3.8 cm. The radius (r) is half of the diameter, so r = 3.8 cm / 2 = 1.9 cm.

Step 2: Use the formula for the volume of a cylinder.
The volume (V) of a cylinder is given by the formula V = π * r^2 * h, where π is approximately 3.14, r is the radius, and h is the height.

Plugging in the values: V = 3.14 * (1.9 cm)^2 * 5.4 cm.

Simplifying the calculation: V ≈ 3.14 * 3.61 cm^2 * 5.4 cm.

Multiplying the values: V ≈ 61.023 cm^3.

Step 3: Add the volume of the metal cylinder to the initial volume of water in the graduated cylinder.
The initial volume of water was given as 56.3 ml. To convert this to cm^3, we know that 1 ml is equivalent to 1 cm^3. Therefore, the initial volume in cm^3 is also 56.3 cm^3.

Finally, we can find the volume reading in the graduated cylinder after the metal cylinder is added by adding the calculated volume of the metal cylinder to the initial volume of water:
Volume reading = Initial volume + Volume of metal cylinder = 56.3 cm^3 + 61.023 cm^3 = 117.323 cm^3.

Therefore, the volume reading in the graduated cylinder after the cylinder is added is approximately 117.323 cm^3.