A spherical steel ball bearing has a diameter of 2.540 cm at 24°C.
(a) What is the diameter when its temperature is raised to 82°C?
(b) What temperature change is required to increase its volume by 1.1%?
I got the first answer right.
i am having trouble understanding how to figure out how much the diameter is increased by when i know how much the total volume is increased by.....
Take the cube root of the volume increase factor
(1.011)^1/3 = 1.0036533.
That will be the diameter increase factor. The increase will be 0.3653%
The temperature of the air outside on a cool morning is 11„aC.What is
this temperature on the Kelvin scale?
To calculate how much the diameter of the steel ball bearing increases when you know how much the volume increases, you need to understand the relationship between volume and diameter for a sphere.
The volume of a sphere is given by the formula:
V = (4/3)πr^3
Where V is the volume and r is the radius of the sphere. Since you have the diameter of the ball bearing, you can use it to find the radius by dividing it by 2.
Now, if the volume of the sphere increases by a certain percentage, you can find the new volume by multiplying the original volume by (1 + percentage increase). In this case, the percentage increase is 1.1%, so you would multiply the original volume by 1 + 0.011.
Once you have the new volume, you can use the formula for the volume of a sphere to find the new radius. Rearrange the formula to solve for r:
r = ((3V) / (4π))^(1/3)
Now, you can calculate the new radius using the new volume. Subtract the original radius from the new radius to find the change in radius. Finally, multiply the change in radius by 2 to get the change in diameter.
Let's calculate:
(a) The temperature change to increase the diameter by a certain amount:
1. Calculate the original volume using the original diameter.
2. Calculate the new volume using the new temperature and the formula V = (4/3)πr^3.
3. Calculate the new radius using the new volume and the formula r = ((3V) / (4π))^(1/3).
4. Calculate the change in radius and multiply it by 2 to get the change in diameter.
(b) The temperature change to increase the volume by a certain percentage:
1. Calculate the original volume using the original diameter.
2. Calculate the new volume by multiplying the original volume by (1 + percentage increase).
3. Calculate the new radius using the new volume and the formula r = ((3V) / (4π))^(1/3).
4. Calculate the change in radius and multiply it by 2 to get the change in diameter.
By following these steps, you should be able to calculate the change in diameter based on the change in volume.