Three circles are externally tangent to one another. The radius of each of the circles is 2 cm. A belt fits tightly around the three circles. Find the length of the belt. Express your answer in terms of pi with an explanation.
πd is the circumference of a circle, so with a diameter of 4 a single circle has a circumference of 4π. 1/3 of each circle is in contact with the belt, so that total part is still 4π. Then, the part of the belt connecting from tangent to tangent is 2 radii, so 3 areas is 12. The belt would then be 12+4π cm.
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3.
Which is greater, the circumference of a circle with radius 3 ft, or the distance around a semicircle with diameter 16 ft? By how much?
A. circle, by 4 ft
B. circle, by 2 ft
C. semicircle, by 4 ft
D. semicircle, by 2 ft
To find the length of the belt, we need to find the circumference of each circle and sum them up.
The circumference of a circle can be found by using the formula:
C = 2πr
Given that the radius of each circle is 2 cm, the circumference of each circle is:
C1 = 2π(2) = 4π cm
C2 = 2π(2) = 4π cm
C3 = 2π(2) = 4π cm
Since the three circles are externally tangent to one another, the belt will pass through the centers of the three circles. The length of the belt will be the sum of the circumferences of the three circles.
Length of the belt = C1 + C2 + C3
= 4π + 4π + 4π
= 12π cm
Therefore, the length of the belt is 12π cm.
To find the length of the belt, we need to calculate the circumference of each circle and then add them together.
The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the radius of each circle is given as 2 cm.
So, the circumference of each circle is C = 2π(2) = 4π cm.
Since the three circles are externally tangent, when the belt is wrapped around them tightly, it will be touching the outer sides of each circle. This means that the length of the belt will be equal to the sum of the circumferences of the three circles.
Adding the circumferences, we get: 4π + 4π + 4π = 12π cm.
Therefore, the length of the belt is 12π cm.