A graduated cylinder with a radius of 3 cm contains water to a height of 9 cm. Yann adds 15 steel balls, each with a diameter of 2.54 cm.



What is the total volume of the contents in the cylinder after the balls are added? Use 3.14 to approximate pi and round your answer to one decimal place.
v=4.3 3,14 3

each ball has volume

4/3 pi * (2.54/2)^3 = 8.58 cm^3

There are 15 of them, so add 15 times that to the volume of water, which is

pi * 3^2 * 9 = 254.47

Note how they coyly avoided saying the balls were 1" in diameter. Saved you the step of doing the conversion to cm.

To find the total volume of the contents in the cylinder after the balls are added, we need to calculate the volume of the water and the volume of the steel balls separately, and then add them together.

The volume of the water in the cylinder can be calculated using the formula for the volume of a cylinder: V = πr^2h, where V is the volume, π is approximately equal to 3.14, r is the radius, and h is the height.

Given that the radius of the cylinder is 3 cm and the height of the water is 9 cm, we can substitute these values into the formula:

V_water = 3.14 * (3 cm)^2 * 9 cm
= 3.14 * 9 cm^3 * 9 cm
= 254.34 cm^3 (rounded to two decimal places)

Next, we need to calculate the volume of each steel ball. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.

Since the diameter of each steel ball is given as 2.54 cm, the radius of each ball is half of the diameter, which is 2.54 cm / 2 = 1.27 cm.

Now, substitute the radius into the formula to calculate the volume of each steel ball:

V_ball = (4/3) * 3.14 * (1.27 cm)^3
= 4.19 * 1.27 cm^3
= 5.30 cm^3 (rounded to two decimal places)

Since there are 15 steel balls, multiply the volume of each ball by the number of balls to get the total volume of the steel balls:

Total_volume_balls = 5.30 cm^3 * 15 balls
= 79.50 cm^3 (rounded to two decimal places)

Finally, to find the total volume of the contents in the cylinder, add the volume of the water and the volume of the steel balls:

Total_volume_contents = V_water + Total_volume_balls
= 254.34 cm^3 + 79.50 cm^3
= 333.84 cm^3 (rounded to two decimal places)

Therefore, the total volume of the contents in the cylinder after the balls are added is approximately 333.84 cm^3.