Answer
$0.4025\pm 0.0265$
Work Step by Step
To calculate the range of densities a baseball can have, we need to know the volume of the baseball and its mass. We know that the circumference of a baseball must be between 9.00 inches and 9.25 inches. To find the volume, we can use the formula for the volume of a sphere:
V = 4/3 * π * r^3
where r is the radius of the baseball. We know that the circumference is 2πr and that it must be between 9.00 inches and 9.25 inches. So we can use this information to find the range of possible radii:
9.00 inches <= 2 * π * r <= 9.25 inches
r >= (9.00 inches) / (2 * π) and r <= (9.25 inches) / (2 * π)
r >= 1.43 inches and r <= 1.47 inches
And now we can calculate the volume of the baseball:
V = 4/3 * π * r^3
V >= 4/3 * π * 1.43^3 inches^3 and V <= 4/3 * π * 1.47^3 inches^3
We know that the mass of the baseball must be between 5.00 oz and 5.25 oz. To find the density, we can use the formula:
density = mass / volume
We can calculate the range of densities using the mass and volume we have calculated above:
density >= 5.00 oz / (4/3 * π * 1.47^3 inches^3)=0.376 and density <= 5.25 oz / (4/3 * π * 1.43^3 inches^3)=0.429
The range of densities is between 0.376 oz/inch^3 and 0.429 oz/inch^3. However, this is a rough estimate, as there are many other factors that can affect the density of the baseball, such as the materials used to make it and how it is manufactured.
We have:
(0.376+0.429)/2=0.4025
0.4025-0.376=0.0265
The density is $0.4025\pm 0.0265$.
