Toy rubber balls are packaged in a cylinder that holds 3 balls. The diameter of each ball is 2.7 cm. Find the volume of the cylinder. Use 3.14 for pi.
The radius of each ball is half the diameter, so it is 2.7 cm / 2 = 1.35 cm.
The formula for the volume of a sphere is V = 4/3 * pi * r^3. So the volume of one ball is V = 4/3 * 3.14 * (1.35 cm)^3 ≈ 12.95 cm^3.
The cylinder holds 3 balls, so the total volume of the 3 balls is 3 * 12.95 cm^3 = 38.85 cm^3.
Therefore, the volume of the cylinder is 38.85 cm^3.
AAAaannndd the bot gets it wrong yet again!
No, the cylinder has to be long enough to hold 3 balls -- that is, it must be three diameters long: 3*2.7 = 8.1 cm.
So the volume of the cylinder is πr^2 h = π * 1.35^2 * 8.1 = 46.377 cm^3
I'm sorry for the mistake in my previous response. Your explanation is correct, and the volume of the cylinder that is able to hold 3 balls is indeed π * 1.35^2 * 8.1 = 46.377 cm^3. Thank you for pointing out the error.
To find the volume of the cylinder, we need to multiply the area of the base by the height.
First, let's find the area of the base of the cylinder, which is the area of a circle. The formula for the area of a circle is A = π * r^2, where π is approximately 3.14 and r is the radius of the circle.
Given that the diameter of each ball is 2.7 cm, we can find the radius by dividing the diameter by 2. So the radius would be 2.7 cm / 2 = 1.35 cm.
Now let's substitute the values into the formula to find the area of the base:
A = 3.14 * (1.35 cm)^2
A ≈ 3.14 * 1.8225 cm^2
A ≈ 5.711925 cm^2 (rounded to 6 decimal places)
Next, we need to determine the height of the cylinder. Since the cylinder can hold 3 balls, it means the height of the cylinder is equal to the height of 3 balls stacked on top of each other. Each ball has a diameter of 2.7 cm, so the height of each ball would also be 2.7 cm.
Therefore, the height of the cylinder is 3 * 2.7 cm = 8.1 cm.
Finally, we can calculate the volume of the cylinder by multiplying the base area by the height:
V = A * h
V = 5.711925 cm^2 * 8.1 cm
V ≈ 46.30720925 cm^3 (rounded to 8 decimal places)
Therefore, the volume of the cylinder is approximately 46.30720925 cm^3.