An order of magnitude is a number of the form 10^n such that can be used to compare magnitudes or quantities.
We will find that the order of magnitude of golf balls that fill a home swimming pool is 10^6
In this case, we want to estimate the number of golf balls that would fill a home swimming pool.
We know that the diameter of a golf ball is D = 42.6mm = 0.0426m
And the volume of a sphere of diameter D is:
V = (4/3)*pi*(D/2)^3
where pi = 3.14
Then the volume of a single golf ball is:
V = (4/3)*3.14*( 0.0426m/2)^3 = 0.00004 m^3
Now we need to find the average volume of a home swimming pool, we can use 48 m^3 (an average one) to do the general math.
To find the number of golf balls that enter in that volume, we need to do the quotient between the volume of the pool and the volume of a single ball:
N = (48 m^3)/(0.00004 m^3) = 1,200,000
If we round this to the next order of magnitude: 10^6 (the exponent is the number of digits at the right of the one)
Then the order of magnitude of golf balls that enter in a home swimming pool is 10^6
If you want to learn more, you can read:
https://brainly.com/question/4953281
