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The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work.
The radius of the rim is half of the diameter, so it is 9 inches.
When the ball goes in the center of the rim, it means the ball is touching the rim at one point.
Since the circumference of the ball is 30 inches, we know that the distance around the ball is 30 inches.
Thus, if the ball is touching the rim at one point, that point must be 30/π (or approximately 9.55) inches above the center of the rim.
Therefore, the distance between the ball and the rim will be the distance from the center of the rim to the point where the ball is touching the rim, which is 9.55 inches.
dang the bot beat me to it
I apologize if I solved it too quickly, but feel free to let me know if you have any other questions or if there's anything else I can help you with.
To find the distance between the ball and the rim, we need to calculate the radius of the basketball rim.
Step 1: The diameter of the rim is given as 18 inches. The diameter is the distance across a circle passing through its center.
Step 2: The radius is half of the diameter. So, we divide the diameter by 2:
Radius = 18 inches / 2 = 9 inches.
Step 3: The circumference of the basketball rim is the distance around the rim. We can use the formula for the circumference of a circle, which is given by the formula:
Circumference = 2 * π * Radius.
Here, π (pi) is a mathematical constant approximately equal to 3.14159.
Step 4: Substituting the value of the radius, we have:
Circumference = 2 * 3.14159 * 9 inches = 56.5487 inches.
Step 5: The ball goes exactly in the center of the rim, so the distance between the ball and the rim would be the radius of the basketball.
Distance between the ball and the rim = 9 inches.
Therefore, the distance between the ball and the rim in a shot where the ball goes exactly in the center of the rim is 9 inches.