What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 plus or minus .09 m?
I know I need to use the formula (4/3)*pi*r3 somewhere in this problem because of the details given, but I'm totally confused.
Add 2.86 + 0.09 and calculate volume.
Subtract 2.86 - 0.09 and calculate voluem. The uncertainty is the difference in the two volumes.
18.89%
To calculate the percent uncertainty in the volume of a spherical beach ball, we need to determine the fractional uncertainty in its radius. The fractional uncertainty is calculated by dividing the uncertainty by the measured value. In this case, the measured value of the radius is 2.86 m, and the uncertainty is 0.09 m.
Fractional uncertainty in radius = (uncertainty / measured value) = 0.09 / 2.86 ≈ 0.0315
Next, we need to calculate the percent uncertainty by multiplying the fractional uncertainty by 100.
Percent uncertainty = (fractional uncertainty) × 100 = 0.0315 × 100 ≈ 3.15%
Therefore, the percent uncertainty in the volume of the spherical beach ball is approximately 3.15%.
To find the percent uncertainty in the volume of a spherical beach ball, you need to determine the relative or percent uncertainty in the radius. Here's how you can do that:
1. Determine the absolute uncertainty in the radius: In this case, the radius has a value of 2.86 m with an uncertainty of ±0.09 m. The absolute uncertainty is half of the range of the uncertainty, which is 0.09 m / 2 = 0.045 m.
2. Calculate the relative or percent uncertainty: To find the percent uncertainty, divide the absolute uncertainty by the measured value of the radius and multiply by 100%. In this case, the percent uncertainty in the radius is (0.045 m / 2.86 m) * 100% = 1.57%.
3. Use the percent uncertainty to calculate the percent uncertainty in the volume: The formula for the volume of a sphere is V = (4/3) * π * r^3. To find the percent uncertainty in the volume, multiply the percent uncertainty in the radius by the exponent of the radius in the formula. In this case, the exponent is 3, so the percent uncertainty in the volume is 3 * 1.57% = 4.71%.
Therefore, the percent uncertainty in the volume of the spherical beach ball is roughly 4.71%.