So you want to calculate the radius of the ball, or some other measurement like diameter or circumference?
I'll just give you the tools, and you can calculate whichever you want, or mean, or need...
There is a simple formula for calculating all of these and "rearranging" the formula allows calculating any of the 3 variables.
First, define the variables:
D=Diameter
r=radius
C=circumference
For any circle (like a Basketball cut in half), C=Pi x D, D=Pi x r^2, and r=D/2. Now these can be rearranged as needed.
If you want to know the radius, then solve for r:
First, D=C/Pi
r=D/2
So Measuring the circumference (C) of the ball, say (arbitrary value. I don't know the 'official' size) 10 inches around the ball.
In this case, if C=10", then D=C/Pi = 10/3.1415, so D=3.183 inches.
r=D/2, so r, the radius = 3.183 / 2 = 1.592 inches.
So for your basketball, measure the circumference, calculate the diameter, then the radius.
I'm taking a risk here in that in general, homework questions are not tolerated here. If this IS for homework, consider this a gift. I probably should have left out the details and just supplied the very basics.
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The inside should be about 20% larger than the radius of the basketball style. Simply calculate the radius of the basketball and multiply times 1.2 to get the ideal radius of the rim. So it will be 6.2 or 6 in.
You find the circumference of a hoop by measuing the daimeter or the radius and then use the formulas. C=pie x radius squared(to the second power) C=pie x diameter
You find the circumference ny measuring around the whole basketball in centimeters.
Juliana