A soccer ball has diameter of 400 mm. A pin is stuck into the ball such that it creates the chord AC, which is 20 mm. What is the distance from the chord formed by the pin, and what is the length of EB? (Hint: CD=radius)
a.)0.125 mm
b.)0.5 mm
c.)0.25 mm
To find the distance from the chord formed by the pin and the length of EB, we can use the properties of a circle.
Let's break down the problem step by step:
Step 1: Determine the radius of the soccer ball.
The diameter of the soccer ball is given as 400 mm. Since the radius is half the diameter, the radius can be calculated as:
Radius (CD) = Diameter / 2 = 400 mm / 2 = 200 mm.
Step 2: Find the distance from the chord formed by the pin (AC) to the center (O) of the soccer ball.
The distance from the chord to the center is perpendicular to the chord and is equal to half the length of the chord. Therefore, the distance from the chord to the center (OD) is:
Distance (OD) = Chord length (AC) / 2 = 20 mm / 2 = 10 mm.
Step 3: Calculate the length of EB.
The length of EB can be found using the Pythagorean Theorem since triangle OEB is a right triangle.
The hypotenuse OE is the radius (CD) = 200 mm, and the length of OD is 10 mm.
Using the Pythagorean Theorem, we have:
EB^2 + OD^2 = OE^2 (from the right triangle OEB)
EB^2 + 10 mm^2 = 200 mm^2
EB^2 = 200 mm^2 - 10 mm^2
EB^2 = 40000 mm^2 - 100 mm^2
EB^2 = 39900 mm^2
EB = √(39900 mm^2) ≈ 199.75 mm ≈ 200 mm (rounded to the nearest mm).
Step 4: Convert the length of EB from mm to meters.
200 mm = 200/1000 meters = 0.2 meters.
Therefore, the distance from the chord formed by the pin to the center of the soccer ball is 10 mm, and the length of EB is 0.2 meters.
Comparing the options:
a.) 0.125 mm - This option does not match the calculated value.
b.) 0.5 mm - This option does not match the calculated value.
c.) 0.25 mm - This option does not match the calculated value.
None of the given options match the calculated values.