I need help with the following problem:
Calculate the upper and lower limits of the volume (in cm^3) of a cylinder 5.2+- 0.1 centimeters long and 1.6+- 0.1 centimeters in diameter. I know I am suppose to plug the numbers in the sphere formula V= pi/4(d) ^2h, but I do not know hot to set the problem up. Note: (subtraction sign suppose to be below the addition symbol, it is plus and minus)
Can't you simply plug in 5.3 for length and 1.7 cm diameter and calculate volume to obtain the upper limit. Then 5.1 long and 1.5 diameter to obtain the lower limit?
I wanted to know can I also use 5.2 and 1.6 for the upper limit?
So when it says upper and lowest I have to take the highest and lowest length and diameter.
To calculate the upper and lower limits of the volume of the cylinder, you need to consider the range of values for both the length and diameter. Given that the length is 5.2 ± 0.1 centimeters and the diameter is 1.6 ± 0.1 centimeters, you can follow these steps:
1. Calculate the upper and lower limits for the length:
- Upper limit: 5.2 + 0.1 = 5.3 cm
- Lower limit: 5.2 - 0.1 = 5.1 cm
2. Calculate the upper and lower limits for the diameter:
- Upper limit: 1.6 + 0.1 = 1.7 cm
- Lower limit: 1.6 - 0.1 = 1.5 cm
3. Use the upper and lower limits to calculate the upper and lower limits of the volume:
- Upper limit: V = (π/4)(1.7 cm)^2(5.3 cm)
- Lower limit: V = (π/4)(1.5 cm)^2(5.1 cm)
4. Calculate the upper and lower limits of the volume using the formulas above:
- Upper limit: V = 14.296 cm^3
- Lower limit: V = 12.236 cm^3
Therefore, the upper and lower limits of the volume of the cylinder are 12.236 cm^3 and 14.296 cm^3, respectively.